{"id":"https://openalex.org/W7131279142","doi":"https://doi.org/10.48550/arxiv.2602.18722","title":"Finite element methods for isometric embedding of Riemannian manifolds","display_name":"Finite element methods for isometric embedding of Riemannian manifolds","publication_year":2026,"publication_date":"2026-02-21","ids":{"openalex":"https://openalex.org/W7131279142","doi":"https://doi.org/10.48550/arxiv.2602.18722"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.18722","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5126670512","display_name":"Guangwei Gao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gao, Guangwei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101998252","display_name":"Kaibo Hu","orcid":"https://orcid.org/0000-0001-9574-9644"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hu, Kaibo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039197834","display_name":"Buyang Li","orcid":"https://orcid.org/0000-0001-7566-3464"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Buyang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5010321711","display_name":"Ganghui Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Ganghui","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.24480000138282776,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.24480000138282776,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.23190000653266907,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.05719999969005585,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.7060999870300293},{"id":"https://openalex.org/keywords/riemannian-geometry","display_name":"Riemannian geometry","score":0.5555999875068665},{"id":"https://openalex.org/keywords/curvature-of-riemannian-manifolds","display_name":"Curvature of Riemannian manifolds","score":0.5203999876976013},{"id":"https://openalex.org/keywords/gaussian-curvature","display_name":"Gaussian curvature","score":0.5123000144958496},{"id":"https://openalex.org/keywords/ricci-curvature","display_name":"Ricci curvature","score":0.5085999965667725},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.4187999963760376},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.40230000019073486},{"id":"https://openalex.org/keywords/information-geometry","display_name":"Information geometry","score":0.40149998664855957},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.39399999380111694}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7092999815940857},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.7060999870300293},{"id":"https://openalex.org/C181104567","wikidata":"https://www.wikidata.org/wiki/Q761383","display_name":"Riemannian geometry","level":2,"score":0.5555999875068665},{"id":"https://openalex.org/C146674193","wikidata":"https://www.wikidata.org/wiki/Q40139","display_name":"Curvature of Riemannian manifolds","level":5,"score":0.5203999876976013},{"id":"https://openalex.org/C16140857","wikidata":"https://www.wikidata.org/wiki/Q945953","display_name":"Gaussian curvature","level":3,"score":0.5123000144958496},{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.5085999965667725},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4724999964237213},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.4187999963760376},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.40230000019073486},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.40149998664855957},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.39399999380111694},{"id":"https://openalex.org/C42448751","wikidata":"https://www.wikidata.org/wiki/Q855622","display_name":"Sectional curvature","level":4,"score":0.36000001430511475},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3522999882698059},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.3433000147342682},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.34220001101493835},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.337799996137619},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.33399999141693115},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3287999927997589},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.32019999623298645},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.31940001249313354},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.30309998989105225},{"id":"https://openalex.org/C4306028","wikidata":"https://www.wikidata.org/wiki/Q2185349","display_name":"Fundamental theorem of Riemannian geometry","level":4,"score":0.29989999532699585},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.2987000048160553},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2897000014781952},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.27559998631477356},{"id":"https://openalex.org/C82457910","wikidata":"https://www.wikidata.org/wiki/Q740207","display_name":"Isometry (Riemannian geometry)","level":2,"score":0.2574000060558319},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.2572999894618988},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.2538999915122986}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.18722","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.18722","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.18722","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.18722","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"isometric":[1,68,136,168,206],"embedding":[2,69,169],"problem":[3,38],"for":[4,95,134],"Riemannian":[5,72,139,210],"manifolds,":[6],"which":[7],"connects":[8],"intrinsic":[9,185],"and":[10,24,33,100,115,156,201],"extrinsic":[11],"geometry,":[12],"is":[13],"a":[14,82,90,102,131,151],"central":[15],"question":[16],"in":[17,47,158,184,204],"differential":[18],"geometry":[19],"with":[20,74,126,144,174],"deep":[21],"theoretical":[22,192],"significance":[23],"wide-ranging":[25],"applications.":[26],"Despite":[27],"extensive":[28],"analytical":[29],"progress,":[30],"the":[31,41,51,60,67,107,113,145,159,167,171,179,191,196,199],"nonlinear":[32],"degenerate":[34],"nature":[35],"of":[36,43,63,70,109,117,138,147,154,170,181,198,208],"this":[37,48,56,110],"has":[39],"hindered":[40],"development":[42],"rigorous":[44,175],"numerical":[45,61,91,119],"analysis":[46,104,193],"area.":[49],"As":[50],"first":[52],"step":[53],"toward":[54],"addressing":[55],"gap,":[57],"we":[58],"study":[59],"approximation":[62],"Weyl's":[64],"problem,":[65],"i.e.,":[66],"two-dimensional":[71],"manifolds":[73,140,211],"positive":[75],"Gaussian":[76],"curvature":[77,186],"into":[78,141],"$\\mathbb{R}^3$,":[79],"by":[80,194],"establishing":[81],"new":[83],"weak":[84,111],"formulation":[85],"that":[86],"naturally":[87,165],"leads":[88],"to":[89,105,150,166],"scheme":[92],"well":[93,122,213],"suited":[94],"high-order":[96],"finite":[97],"element":[98],"discretization,":[99],"conducting":[101],"systematic":[103],"prove":[106],"well-posedness":[108],"formulation,":[112],"existence":[114],"uniqueness":[116],"its":[118,124,202],"solution,":[120],"as":[121,123,212,214],"convergence":[125,197],"error":[127,176],"estimates.":[128],"This":[129],"provides":[130],"foundational":[132],"framework":[133,162],"computing":[135],"embeddings":[137,207],"Euclidean":[142],"space,":[143],"goal":[146],"extending":[148],"it":[149],"broader":[152],"range":[153],"cases":[155],"applications":[157],"future.":[160],"Our":[161],"also":[163],"extends":[164],"Ricci":[172,215],"flow,":[173],"estimates,":[177],"enabling":[178],"visualization":[180],"geometric":[182],"evolutions":[183],"flows.":[187,216],"Numerical":[188],"experiments":[189],"support":[190],"demonstrating":[195],"method":[200],"effectiveness":[203],"simulating":[205],"given":[209]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-02-25T00:00:00"}
