{"id":"https://openalex.org/W1992785155","doi":"https://doi.org/10.1137/060649495","title":"As Flat As Possible","display_name":"As Flat As Possible","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W1992785155","doi":"https://doi.org/10.1137/060649495","mag":"1992785155"},"language":"en","primary_location":{"id":"doi:10.1137/060649495","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060649495","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1767&context=hmc_fac_pub","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015813554","display_name":"Jon Jacobsen","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jon Jacobsen","raw_affiliation_strings":["jacobsen@math.hmc.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"jacobsen@math.hmc.edu#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5015813554"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4337,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.59027439,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"49","issue":"3","first_page":"491","last_page":"507"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9980999827384949,"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"}},"topics":[{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9980999827384949,"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"}},{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9926000237464905,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/partial-differential-equation","display_name":"Partial differential equation","score":0.6280274391174316},{"id":"https://openalex.org/keywords/twist","display_name":"Twist","score":0.5496212244033813},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.5492331385612488},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5228719711303711},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.48767101764678955},{"id":"https://openalex.org/keywords/theme","display_name":"Theme (computing)","score":0.4419589936733246},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.43060699105262756},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4278672933578491},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4226316809654236},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.373969167470932},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3158750832080841},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21618258953094482},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15844881534576416},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.08553794026374817},{"id":"https://openalex.org/keywords/world-wide-web","display_name":"World Wide Web","score":0.060637861490249634}],"concepts":[{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6280274391174316},{"id":"https://openalex.org/C2776196297","wikidata":"https://www.wikidata.org/wiki/Q17138781","display_name":"Twist","level":2,"score":0.5496212244033813},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.5492331385612488},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5228719711303711},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.48767101764678955},{"id":"https://openalex.org/C33566652","wikidata":"https://www.wikidata.org/wiki/Q1065927","display_name":"Theme (computing)","level":2,"score":0.4419589936733246},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.43060699105262756},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4278672933578491},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4226316809654236},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.373969167470932},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3158750832080841},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21618258953094482},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15844881534576416},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.08553794026374817},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.060637861490249634},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/060649495","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060649495","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","raw_type":"journal-article"},{"id":"pmh:oai:scholarship.claremont.edu:hmc_fac_pub-1767","is_oa":true,"landing_page_url":"https://scholarship.claremont.edu/hmc_fac_pub/762","pdf_url":"https://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1767&context=hmc_fac_pub","source":{"id":"https://openalex.org/S4306401604","display_name":"Scholarship @ Claremont (The Claremont Colleges)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I872248612","host_organization_name":"Claremont Colleges","host_organization_lineage":["https://openalex.org/I872248612"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"All HMC Faculty Publications and Research","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.936.8340","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.936.8340","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://scholarship.claremont.edu/cgi/viewcontent.cgi?article%3D1767%26context%3Dhmc_fac_pub","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:scholarship.claremont.edu:hmc_fac_pub-1767","is_oa":true,"landing_page_url":"https://scholarship.claremont.edu/hmc_fac_pub/762","pdf_url":"https://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1767&context=hmc_fac_pub","source":{"id":"https://openalex.org/S4306401604","display_name":"Scholarship @ Claremont (The Claremont Colleges)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I872248612","host_organization_name":"Claremont Colleges","host_organization_lineage":["https://openalex.org/I872248612"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"All HMC Faculty Publications and Research","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1992785155.pdf","grobid_xml":"https://content.openalex.org/works/W1992785155.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W652387816","https://openalex.org/W1483726821","https://openalex.org/W1491650242","https://openalex.org/W1509346826","https://openalex.org/W1544375930","https://openalex.org/W1565212980","https://openalex.org/W1582131183","https://openalex.org/W2066787099","https://openalex.org/W2082052570","https://openalex.org/W2139502098","https://openalex.org/W3021722416","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2123186262","https://openalex.org/W2802274723","https://openalex.org/W2001543340","https://openalex.org/W2559572050","https://openalex.org/W2003672595","https://openalex.org/W2063425968","https://openalex.org/W2098164907","https://openalex.org/W173045509","https://openalex.org/W2765820228","https://openalex.org/W1975538847"],"abstract_inverted_index":{"How":[0],"does":[1,21],"one":[2,43,46],"determine":[3],"a":[4,56,67,82,86],"surface":[5,68],"which":[6],"is":[7],"as":[8,10,13,26,28,70,74,76],"flat":[9,27],"possible,":[11],"such":[12],"those":[14],"created":[15],"by":[16],"soap":[17],"film":[18],"surfaces?":[19],"What":[20],"it":[22,73],"mean":[23],"to":[24,65,71,84],"be":[25],"possible?":[29],"In":[30],"this":[31,35,52],"paper":[32],"we":[33,54],"address":[34],"question":[36,61],"from":[37],"two":[38],"distinct":[39],"points":[40],"of":[41,89,104,106],"view,":[42],"local":[44],"and":[45,62,96,101,109],"global":[47],"in":[48,92],"nature.":[49],"Continuing":[50],"with":[51],"theme,":[53],"put":[55],"temporal":[57],"twist":[58],"on":[59],"the":[60],"ask":[63],"how":[64],"evolve":[66],"so":[69],"flatten":[72],"efficiently":[75],"possible.":[77],"This":[78],"elementary":[79],"discussion":[80],"provides":[81],"platform":[83],"introduce":[85],"wide":[87],"range":[88],"advanced":[90],"topics":[91],"partial":[93,111],"differential":[94,112],"equations":[95],"helps":[97],"students":[98],"build":[99],"geometric":[100],"analytic":[102],"understanding":[103],"solutions":[105],"certain":[107],"elliptic":[108],"parabolic":[110],"equations.":[113]},"counts_by_year":[{"year":2015,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
