{"id":"https://openalex.org/W2203469805","doi":"https://doi.org/10.1007/s10208-019-09439-7","title":"Reconstruction and Interpolation of Manifolds. I: The Geometric Whitney Problem","display_name":"Reconstruction and Interpolation of Manifolds. I: The Geometric Whitney Problem","publication_year":2019,"publication_date":"2019-11-13","ids":{"openalex":"https://openalex.org/W2203469805","doi":"https://doi.org/10.1007/s10208-019-09439-7","mag":"2203469805"},"language":"lv","primary_location":{"id":"doi:10.1007/s10208-019-09439-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-019-09439-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-019-09439-7.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10208-019-09439-7.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037466938","display_name":"Charles Fefferman","orcid":"https://orcid.org/0000-0002-9565-6488"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Charles Fefferman","raw_affiliation_strings":["Mathematics department, Princeton University, Princeton, USA"],"affiliations":[{"raw_affiliation_string":"Mathematics department, Princeton University, Princeton, USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088158552","display_name":"Sergei Ivanov","orcid":"https://orcid.org/0000-0003-1637-8545"},"institutions":[{"id":"https://openalex.org/I2800906181","display_name":"St. Petersburg Department of Steklov Institute of Mathematics","ror":"https://ror.org/030h9s280","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I2800906181","https://openalex.org/I4210124601"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Sergei Ivanov","raw_affiliation_strings":["St. Petersburg Department of Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia"],"affiliations":[{"raw_affiliation_string":"St. Petersburg Department of Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia","institution_ids":["https://openalex.org/I2800906181"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111481047","display_name":"Yaroslav Kurylev","orcid":null},"institutions":[{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Yaroslav Kurylev","raw_affiliation_strings":["Department of Mathematics, University College, London, London, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University College, London, London, UK","institution_ids":["https://openalex.org/I45129253"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052627284","display_name":"Matti Lassas","orcid":"https://orcid.org/0000-0003-2043-3156"},"institutions":[{"id":"https://openalex.org/I1323065761","display_name":"Statistics Finland","ror":"https://ror.org/01n1rg855","country_code":"FI","type":"other","lineage":["https://openalex.org/I1323065761"]},{"id":"https://openalex.org/I133731052","display_name":"University of Helsinki","ror":"https://ror.org/040af2s02","country_code":"FI","type":"education","lineage":["https://openalex.org/I133731052"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Matti Lassas","raw_affiliation_strings":["*Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland"],"affiliations":[{"raw_affiliation_string":"*Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland","institution_ids":["https://openalex.org/I1323065761","https://openalex.org/I133731052"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029536777","display_name":"Hariharan Narayanan","orcid":"https://orcid.org/0000-0003-0568-7350"},"institutions":[{"id":"https://openalex.org/I11947397","display_name":"Tata Institute of Fundamental Research","ror":"https://ror.org/03ht1xw27","country_code":"IN","type":"education","lineage":["https://openalex.org/I11947397","https://openalex.org/I2799351866","https://openalex.org/I3149292468"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Hariharan Narayanan","raw_affiliation_strings":["School of Technology and Computer Science, Tata Institute for Fundamental Research, Mumbai, India"],"affiliations":[{"raw_affiliation_string":"School of Technology and Computer Science, Tata Institute for Fundamental Research, Mumbai, India","institution_ids":["https://openalex.org/I11947397"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5037466938"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":1.8932,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.82463768,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"20","issue":"5","first_page":"1035","last_page":"1133"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9810000061988831,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12417","display_name":"Morphological variations and asymmetry","score":0.9805999994277954,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8113828301429749},{"id":"https://openalex.org/keywords/pseudo-riemannian-manifold","display_name":"Pseudo-Riemannian manifold","score":0.5874263644218445},{"id":"https://openalex.org/keywords/riemannian-geometry","display_name":"Riemannian geometry","score":0.5095839500427246},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.49912095069885254},{"id":"https://openalex.org/keywords/tangent-space","display_name":"Tangent space","score":0.48500916361808777},{"id":"https://openalex.org/keywords/submanifold","display_name":"Submanifold","score":0.4842819571495056},{"id":"https://openalex.org/keywords/sectional-curvature","display_name":"Sectional curvature","score":0.47284987568855286},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46952953934669495},{"id":"https://openalex.org/keywords/hausdorff-distance","display_name":"Hausdorff distance","score":0.46913620829582214},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.46759694814682007},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.4502696990966797},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.44846659898757935},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.44568079710006714},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.4346464276313782},{"id":"https://openalex.org/keywords/ricci-curvature","display_name":"Ricci curvature","score":0.42897146940231323},{"id":"https://openalex.org/keywords/statistical-manifold","display_name":"Statistical manifold","score":0.41141730546951294},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4094693660736084},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3764388859272003},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.36954236030578613},{"id":"https://openalex.org/keywords/scalar-curvature","display_name":"Scalar curvature","score":0.2899918258190155},{"id":"https://openalex.org/keywords/information-geometry","display_name":"Information geometry","score":0.27234065532684326},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2556889057159424},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18703493475914001}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8113828301429749},{"id":"https://openalex.org/C121705324","wikidata":"https://www.wikidata.org/wiki/Q1510587","display_name":"Pseudo-Riemannian manifold","level":4,"score":0.5874263644218445},{"id":"https://openalex.org/C181104567","wikidata":"https://www.wikidata.org/wiki/Q761383","display_name":"Riemannian geometry","level":2,"score":0.5095839500427246},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.49912095069885254},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.48500916361808777},{"id":"https://openalex.org/C151300846","wikidata":"https://www.wikidata.org/wiki/Q125539","display_name":"Submanifold","level":2,"score":0.4842819571495056},{"id":"https://openalex.org/C42448751","wikidata":"https://www.wikidata.org/wiki/Q855622","display_name":"Sectional curvature","level":4,"score":0.47284987568855286},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46952953934669495},{"id":"https://openalex.org/C141898687","wikidata":"https://www.wikidata.org/wiki/Q1501997","display_name":"Hausdorff distance","level":2,"score":0.46913620829582214},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.46759694814682007},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4502696990966797},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.44846659898757935},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.44568079710006714},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.4346464276313782},{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.42897146940231323},{"id":"https://openalex.org/C169391604","wikidata":"https://www.wikidata.org/wiki/Q7604402","display_name":"Statistical manifold","level":5,"score":0.41141730546951294},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4094693660736084},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3764388859272003},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.36954236030578613},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.2899918258190155},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.27234065532684326},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2556889057159424},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18703493475914001},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1007/s10208-019-09439-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-019-09439-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-019-09439-7.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1508.00674","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1508.00674","pdf_url":"https://arxiv.org/pdf/1508.00674","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2203469805","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1508.00674.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:eprints.ucl.ac.uk.OAI2:1522488","is_oa":false,"landing_page_url":"https://discovery.ucl.ac.uk/id/eprint/1522488/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400024","display_name":"UCL Discovery (University College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45129253","host_organization_name":"University College London","host_organization_lineage":["https://openalex.org/I45129253"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"     (2015)     ","raw_type":"Working / discussion paper"},{"id":"pmh:oai:helda.helsinki.fi:10138/324867","is_oa":true,"landing_page_url":"http://hdl.handle.net/10138/324867","pdf_url":null,"source":{"id":"https://openalex.org/S4210213322","display_name":"Ty\u00f6v\u00e4entutkimus Vuosikirja","issn_l":"0784-1272","issn":["0784-1272","1459-7780"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"doi:10.48550/arxiv.1508.00674","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1508.00674","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s10208-019-09439-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-019-09439-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-019-09439-7.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G1555727046","display_name":null,"funder_award_id":"DMS-1265524","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2545269695","display_name":null,"funder_award_id":"1265524","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4093763636","display_name":null,"funder_award_id":"DMS-1265524","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5809100787","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6071252945","display_name":null,"funder_award_id":"FA9550-12","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G7999580237","display_name":null,"funder_award_id":"FA9550-12-1","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320310086","display_name":"Helsingin Yliopisto","ror":"https://ror.org/040af2s02"},{"id":"https://openalex.org/F4320310467","display_name":"Helsingin ja Uudenmaan Sairaanhoitopiiri","ror":"https://ror.org/020cpqb94"},{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2203469805.pdf","grobid_xml":"https://content.openalex.org/works/W2203469805.grobid-xml"},"referenced_works_count":106,"referenced_works":["https://openalex.org/W560409768","https://openalex.org/W568942680","https://openalex.org/W613352991","https://openalex.org/W1242194915","https://openalex.org/W1258514360","https://openalex.org/W1484696448","https://openalex.org/W1496274530","https://openalex.org/W1510073064","https://openalex.org/W1544179784","https://openalex.org/W1570089119","https://openalex.org/W1570665229","https://openalex.org/W1595132914","https://openalex.org/W1602064551","https://openalex.org/W1609345135","https://openalex.org/W1632601927","https://openalex.org/W1671098680","https://openalex.org/W1802177642","https://openalex.org/W1820771660","https://openalex.org/W1941524829","https://openalex.org/W1955705852","https://openalex.org/W1966949944","https://openalex.org/W1972141460","https://openalex.org/W1973400731","https://openalex.org/W1974363244","https://openalex.org/W1976883205","https://openalex.org/W1980267728","https://openalex.org/W1981923740","https://openalex.org/W1986198949","https://openalex.org/W1986817086","https://openalex.org/W1987723734","https://openalex.org/W1992901553","https://openalex.org/W1997105460","https://openalex.org/W1999760688","https://openalex.org/W2001141328","https://openalex.org/W2002688463","https://openalex.org/W2003539828","https://openalex.org/W2026429431","https://openalex.org/W2027673210","https://openalex.org/W2027676349","https://openalex.org/W2029412937","https://openalex.org/W2033733331","https://openalex.org/W2038292677","https://openalex.org/W2044060118","https://openalex.org/W2045487399","https://openalex.org/W2047833390","https://openalex.org/W2049176462","https://openalex.org/W2049795217","https://openalex.org/W2052797733","https://openalex.org/W2053186076","https://openalex.org/W2054715297","https://openalex.org/W2058304130","https://openalex.org/W2060257269","https://openalex.org/W2071128523","https://openalex.org/W2077776048","https://openalex.org/W2078817916","https://openalex.org/W2079746361","https://openalex.org/W2082658753","https://openalex.org/W2083493892","https://openalex.org/W2085373658","https://openalex.org/W2086919648","https://openalex.org/W2093017678","https://openalex.org/W2096496077","https://openalex.org/W2102958772","https://openalex.org/W2112148214","https://openalex.org/W2118123209","https://openalex.org/W2119548491","https://openalex.org/W2134086356","https://openalex.org/W2134420283","https://openalex.org/W2142204634","https://openalex.org/W2156316288","https://openalex.org/W2156718197","https://openalex.org/W2156838815","https://openalex.org/W2157206294","https://openalex.org/W2163581538","https://openalex.org/W2167769608","https://openalex.org/W2294798173","https://openalex.org/W2313098395","https://openalex.org/W2318624729","https://openalex.org/W2333620035","https://openalex.org/W2494963564","https://openalex.org/W2587317868","https://openalex.org/W2892948875","https://openalex.org/W2962757511","https://openalex.org/W2963693826","https://openalex.org/W2963856018","https://openalex.org/W2963910409","https://openalex.org/W2964203384","https://openalex.org/W3013880646","https://openalex.org/W3038588914","https://openalex.org/W3040283615","https://openalex.org/W3102292222","https://openalex.org/W3105264615","https://openalex.org/W4230172292","https://openalex.org/W4233075542","https://openalex.org/W4233378206","https://openalex.org/W4235476591","https://openalex.org/W4236657544","https://openalex.org/W4236754516","https://openalex.org/W4238805501","https://openalex.org/W4242771523","https://openalex.org/W4253175466","https://openalex.org/W4253695550","https://openalex.org/W4253840677","https://openalex.org/W6639898810","https://openalex.org/W6674723449","https://openalex.org/W6733111253"],"related_works":["https://openalex.org/W2985958162","https://openalex.org/W1987634595","https://openalex.org/W2137842291","https://openalex.org/W2060233727","https://openalex.org/W2106506629","https://openalex.org/W2477002515","https://openalex.org/W2950902931","https://openalex.org/W2963949927","https://openalex.org/W3003694056","https://openalex.org/W2244240907","https://openalex.org/W2950749539","https://openalex.org/W2890370060","https://openalex.org/W2953347060","https://openalex.org/W2057536670","https://openalex.org/W2283361197","https://openalex.org/W2151393998","https://openalex.org/W2952550597","https://openalex.org/W2896431968","https://openalex.org/W1511139817","https://openalex.org/W1628709819"],"abstract_inverted_index":{"Abstract":[0],"We":[1,138,162,261],"study":[2],"the":[3,129,143,149,176,215,233,243,267,276,285,315],"geometric":[4,268],"Whitney":[5,269,316],"problem":[6,41,270,279],"on":[7,311],"how":[8],"a":[9,22,52,89,125,169,182,186,220,249,272,312,340],"Riemannian":[10,126,157,183,307],"manifold":[11,46,49,127,184,277],"(":[12],"M":[13],",":[14,73],"g":[15],")":[16],"can":[17,153,172,239],"be":[18,85,154,173,240],"constructed":[19,86],"to":[20,45,84,87,142,166,339],"approximate":[21,88],"metric":[23,150,170,245,273,300],"space":[24,171,274],"$$(X,d_X)$$":[25],"<mml:math":[26,60,75,95,328],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[27,61,76,96,329],"<mml:mrow>":[28,62,66,77,98,331],"<mml:mo>(</mml:mo>":[29],"<mml:mi>X</mml:mi>":[30,34],"<mml:mo>,</mml:mo>":[31],"<mml:msub>":[32],"<mml:mi>d</mml:mi>":[33],"</mml:msub>":[35],"<mml:mo>)</mml:mo>":[36],"</mml:mrow>":[37,68,71,81,100,333],"</mml:math>":[38,72,82,103,336],".":[39,104],"This":[40],"is":[42],"closely":[43],"related":[44],"interpolation":[47,293],"(or":[48],"reconstruction)":[50],"where":[51,319],"smooth":[53,341],"n":[54],"-dimensional":[55],"submanifold":[56],"$$S\\subset":[57],"{{\\mathbb":[58],"{R}}}^m$$":[59,94,327],"<mml:mi>S</mml:mi>":[63],"<mml:mo>\u2282</mml:mo>":[64],"<mml:msup>":[65,97,330],"<mml:mi>R</mml:mi>":[67,99,332],"<mml:mi>m</mml:mi>":[69,78,101,334],"</mml:msup>":[70,102,335],"$$m&gt;n$$":[74],"<mml:mo>&gt;</mml:mo>":[79],"<mml:mi>n</mml:mi>":[80],"needs":[83],"point":[90],"cloud":[91],"in":[92,109,115,120,175,242,280,325],"$${{\\mathbb":[93,326],"These":[105],"questions":[106],"are":[107,209,295,309,323],"encountered":[108,119],"differential":[110],"geometry,":[111],"machine":[112],"learning,":[113],"and":[114,136,189,195,252,257,275,283,302,337],"many":[116],"inverse":[117],"problems":[118,294],"applications.":[121],"The":[122,291,304],"determination":[123],"of":[124,131,185,207,214,223,235,248,288,314],"includes":[128],"construction":[130,318],"its":[132],"topology,":[133],"differentiable":[134],"structure,":[135],"metric.":[137],"give":[139,163,219],"constructive":[140],"solutions":[141],"above":[144,292],"problems.":[145],"Moreover,":[146,230],"we":[147,199,218,231],"characterize":[148,232],"spaces":[151,225,237],"that":[152,168,201,238,265],"approximated,":[155,174],"by":[156,181,246],"manifolds":[158,308],"with":[159,190,204,226,253],"bounded":[160,191,254],"geometry:":[161],"sufficient":[164],"conditions":[165],"ensure":[167],"Gromov\u2013Hausdorff":[177],"or":[178],"quasi-isometric":[179],"sense,":[180],"fixed":[187,250],"dimension":[188,251],"diameter,":[192],"sectional":[193],"curvature,":[194],"injectivity":[196,259],"radius.":[197,260],"Also,":[198],"show":[200],"similar":[202],"conditions,":[203],"modified":[205],"values":[206],"parameters,":[208],"necessary.":[210],"As":[211],"an":[212],"application":[213],"main":[216],"results,":[217],"new":[221],"characterization":[222],"Alexandrov":[224],"two-sided":[227],"curvature":[228],"bounds.":[229],"subsets":[234],"Euclidean":[236,281],"approximated":[241],"Hausdorff":[244],"submanifolds":[247],"principal":[255],"curvatures":[256],"normal":[258],"develop":[262],"algorithmic":[263],"procedures":[264],"solve":[266],"for":[271,298,306],"reconstruction":[278],"space,":[282],"estimate":[284],"computational":[286],"complexity":[287],"these":[289],"procedures.":[290],"also":[296],"studied":[297],"unbounded":[299],"sets":[301],"manifolds.":[303],"results":[305],"based":[310],"generalization":[313],"embedding":[317],"approximative":[320],"coordinate":[321],"charts":[322],"embedded":[324],"interpolated":[338],"submanifold.":[342]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
