{"id":"https://openalex.org/W7216195459","doi":"https://doi.org/10.48550/arxiv.2610.01550","title":"The sphere is the only closed surface satisfying the fixed-width Archimedean property","display_name":"The sphere is the only closed surface satisfying the fixed-width Archimedean property","publication_year":2026,"publication_date":"2026-10-01","ids":{"openalex":"https://openalex.org/W7216195459","doi":"https://doi.org/10.48550/arxiv.2610.01550"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.01550","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.01550","pdf_url":"https://arxiv.org/pdf/2610.01550","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.01550","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052180126","display_name":"Mijia Lai","orcid":"https://orcid.org/0000-0002-8316-6043","observed_orcids":["https://orcid.org/0000-0002-8316-6043"]},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lai, Mijia","raw_affiliation_strings":["SCHOOL OF MATHEMATICAL SCIENCES , SHANGHAI JIAO TONG UNIVERSITY , SHANGHAI 200240 , CHINA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SCHOOL OF MATHEMATICAL SCIENCES , SHANGHAI JIAO TONG UNIVERSITY , SHANGHAI 200240 , CHINA","institution_ids":["https://openalex.org/I183067930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5052180126"],"corresponding_institution_ids":["https://openalex.org/I183067930"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.7148000001907349,"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"}},"topics":[{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.7148000001907349,"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"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.21080000698566437,"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"}},{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.050200000405311584,"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/unit-sphere","display_name":"unit sphere","score":0.8100000023841858},{"id":"https://openalex.org/keywords/surface-area","display_name":"surface area","score":0.5049999952316284},{"id":"https://openalex.org/keywords/parallel-planes","display_name":"parallel planes","score":0.6359999775886536},{"id":"https://openalex.org/keywords/differential-geometry-of-surfaces","display_name":"differential geometry of surfaces","score":0.5889999866485596}],"concepts":[{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.7688000202178955},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.7070000171661377},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.6578999757766724},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.631600022315979},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.5166000127792358},{"id":"https://openalex.org/C148189969","wikidata":"https://www.wikidata.org/wiki/Q146657","display_name":"Great circle","level":2,"score":0.5102999806404114},{"id":"https://openalex.org/C164953516","wikidata":"https://www.wikidata.org/wiki/Q320357","display_name":"Closed set","level":2,"score":0.38989999890327454},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.37439998984336853},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36000001430511475},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3458999991416931},{"id":"https://openalex.org/C84316537","wikidata":"https://www.wikidata.org/wiki/Q36255","display_name":"Unit vector","level":2,"score":0.3248000144958496},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3084000051021576},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.2896000146865845},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.2782999873161316},{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.257099986076355}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.01550","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.01550","pdf_url":"https://arxiv.org/pdf/2610.01550","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2610.01550","doi":"https://doi.org/10.48550/arxiv.2610.01550","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.01550","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.01550","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.01550","pdf_url":"https://arxiv.org/pdf/2610.01550","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7216195459.pdf","grobid_xml":"https://content.openalex.org/works/W7216195459.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W1866311589","https://openalex.org/W1996534243","https://openalex.org/W2062668667","https://openalex.org/W2316348307"],"related_works":["https://openalex.org/W7220698660","https://openalex.org/W2062225293","https://openalex.org/W2060634676","https://openalex.org/W2071842447","https://openalex.org/W2004104994","https://openalex.org/W1722103031","https://openalex.org/W2062783233","https://openalex.org/W7117103032","https://openalex.org/W2034320500","https://openalex.org/W2020451100"],"abstract_inverted_index":{"Among":[0],"Archimedes'":[1],"many":[2],"celebrated":[3],"discoveries":[4],"is":[5],"a":[6,26,51],"striking":[7],"fact:":[8],"the":[9,12,21,47],"region":[10],"of":[11],"unit":[13,48],"sphere":[14,22,49],"between":[15],"two":[16],"parallel":[17],"planes,":[18],"both":[19],"meeting":[20],"and":[23],"separated":[24],"by":[25],"distance":[27],"$h$,":[28],"has":[29],"area":[30],"$2\u03c0h$.":[31],"We":[32],"prove":[33],"that,":[34],"among":[35],"connected":[36],"smooth":[37],"closed":[38],"embedded":[39],"surfaces":[40],"in":[41],"$\\mathbb":[42],"R^3$,":[43],"this":[44],"property":[45],"characterizes":[46],"for":[50],"single":[52],"fixed":[53],"width.":[54]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-03T00:00:00"}