{"id":"https://openalex.org/W7223693563","doi":"https://doi.org/10.48550/arxiv.2610.32447","title":"Characterizations of the plane and the catenoid as capillary minimal surfaces","display_name":"Characterizations of the plane and the catenoid as capillary minimal surfaces","publication_year":2026,"publication_date":"2026-10-23","ids":{"openalex":"https://openalex.org/W7223693563","doi":"https://doi.org/10.48550/arxiv.2610.32447"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.32447","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.32447","pdf_url":"https://arxiv.org/pdf/2610.32447","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/2610.32447","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084631483","display_name":"Eungbeom Yeon","orcid":"https://orcid.org/0009-0004-4187-8095","observed_orcids":["https://orcid.org/0009-0004-4187-8095"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yeon, Eungbeom","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5084631483"],"corresponding_institution_ids":[],"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":0.9990000128746033,"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":0.9990000128746033,"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":0.00039999998989515007,"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/T10304","display_name":"Geometric and Algebraic Topology","score":9.999999747378752e-05,"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/catenoid","display_name":"catenoid","score":0.8840000033378601},{"id":"https://openalex.org/keywords/plane","display_name":"plane","score":0.7799999713897705},{"id":"https://openalex.org/keywords/finite-total-curvature","display_name":"finite total curvature","score":0.8159999847412109},{"id":"https://openalex.org/keywords/hopf-differential","display_name":"Hopf differential","score":0.996999979019165},{"id":"https://openalex.org/keywords/gauss-map","display_name":"Gauss map","score":0.7149999737739563},{"id":"https://openalex.org/keywords/second-fundamental-form","display_name":"second fundamental form","score":0.8820000290870667},{"id":"https://openalex.org/keywords/free-boundary-minimal-surfaces","display_name":"free boundary minimal surfaces","score":0.9459999799728394},{"id":"https://openalex.org/keywords/nonexistence-results","display_name":"non-existence results","score":0.7919999957084656},{"id":"https://openalex.org/keywords/vertices","display_name":"vertices","score":0.32899999618530273}],"concepts":[{"id":"https://openalex.org/C30707913","wikidata":"https://www.wikidata.org/wiki/Q1545397","display_name":"Minimal surface","level":2,"score":0.8489999771118164},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6503999829292297},{"id":"https://openalex.org/C128688156","wikidata":"https://www.wikidata.org/wiki/Q5163611","display_name":"Constant-mean-curvature surface","level":5,"score":0.6362000107765198},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5196999907493591},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.49869999289512634},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4927999973297119},{"id":"https://openalex.org/C176688298","wikidata":"https://www.wikidata.org/wiki/Q1072483","display_name":"Helicoid","level":2,"score":0.48570001125335693},{"id":"https://openalex.org/C2776441312","wikidata":"https://www.wikidata.org/wiki/Q575710","display_name":"Gauss map","level":2,"score":0.474700003862381},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.46480000019073486},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.4528000056743622},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.44029998779296875},{"id":"https://openalex.org/C196806460","wikidata":"https://www.wikidata.org/wiki/Q188603","display_name":"Capillary action","level":2,"score":0.4388999938964844},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.42480000853538513},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.40400001406669617},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.39010000228881836},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.38960000872612},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.3840999901294708},{"id":"https://openalex.org/C204575570","wikidata":"https://www.wikidata.org/wiki/Q207476","display_name":"Holomorphic function","level":2,"score":0.37119999527931213},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.33809998631477356},{"id":"https://openalex.org/C16063025","wikidata":"https://www.wikidata.org/wiki/Q4370338","display_name":"Total curvature","level":5,"score":0.3239000141620636},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.3037000000476837},{"id":"https://openalex.org/C16140857","wikidata":"https://www.wikidata.org/wiki/Q945953","display_name":"Gaussian curvature","level":3,"score":0.2930999994277954},{"id":"https://openalex.org/C119830904","wikidata":"https://www.wikidata.org/wiki/Q233220","display_name":"Second fundamental form","level":4,"score":0.29179999232292175},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.27160000801086426},{"id":"https://openalex.org/C77461463","wikidata":"https://www.wikidata.org/wiki/Q7827201","display_name":"Torsion (gastropod)","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C72550971","wikidata":"https://www.wikidata.org/wiki/Q5035397","display_name":"Capillary surface","level":3,"score":0.2671000063419342},{"id":"https://openalex.org/C161794534","wikidata":"https://www.wikidata.org/wiki/Q177493","display_name":"Gauss","level":2,"score":0.2624000012874603},{"id":"https://openalex.org/C199068039","wikidata":"https://www.wikidata.org/wiki/Q574523","display_name":"Immersion (mathematics)","level":2,"score":0.2556999921798706},{"id":"https://openalex.org/C85641259","wikidata":"https://www.wikidata.org/wiki/Q290042","display_name":"Turn (biochemistry)","level":2,"score":0.250900000333786}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.32447","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.32447","pdf_url":"https://arxiv.org/pdf/2610.32447","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.2610.32447","doi":"https://doi.org/10.48550/arxiv.2610.32447","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.32447","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.32447","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.32447","pdf_url":"https://arxiv.org/pdf/2610.32447","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/W7223693563.pdf","grobid_xml":"https://content.openalex.org/works/W7223693563.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1567841374","https://openalex.org/W1969228344","https://openalex.org/W1972732705","https://openalex.org/W1978682653","https://openalex.org/W1980658152","https://openalex.org/W1987360817","https://openalex.org/W1998463340","https://openalex.org/W2013339216","https://openalex.org/W2024581785","https://openalex.org/W2093228106","https://openalex.org/W2139565931","https://openalex.org/W2149597717","https://openalex.org/W2314082730","https://openalex.org/W2329625282","https://openalex.org/W2416207158","https://openalex.org/W4390140102"],"related_works":["https://openalex.org/W2416207158","https://openalex.org/W7119408674","https://openalex.org/W4388575799","https://openalex.org/W2977372414","https://openalex.org/W2013339216","https://openalex.org/W4417452915","https://openalex.org/W3016055298","https://openalex.org/W2997416149","https://openalex.org/W1712614923","https://openalex.org/W2092047840"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,61,72,109],"prove":[4,86],"that":[5],"an":[6,111],"annular":[7,90],"capillary":[8,118],"minimal":[9,93,119],"surface":[10],"outside":[11],"the":[12,31,36,43,46,50,63,74,81,100],"unit":[13],"ball":[14],"in":[15,77],"$\\mathbb{R}^3$":[16],"with":[17,95,121],"one":[18,96],"complete":[19],"embedded":[20],"end":[21,97,101],"and":[22,53],"finite":[23],"total":[24],"curvature":[25],"must":[26],"be":[27],"either":[28],"part":[29,34],"of":[30,35,45,102,114],"plane":[32],"or":[33],"catenoid.":[37],"The":[38],"proofs":[39],"are":[40],"based":[41],"on":[42,117],"use":[44],"Weierstrass":[47],"data":[48],"through":[49],"Hopf":[51],"differential":[52],"associated":[54],"holomorphic":[55],"functions.":[56],"For":[57],"a":[58,69],"planar":[59],"end,":[60,71],"control":[62],"second":[64],"fundamental":[65],"form,":[66],"while":[67],"for":[68,89],"catenoidal":[70],"analyze":[73],"Gauss":[75],"map":[76],"more":[78],"detail":[79],"using":[80],"boundary":[82,92],"condition.":[83],"We":[84],"also":[85],"nonexistence":[87],"results":[88],"free":[91],"surfaces":[94,120],"asymptotic":[98],"to":[99],"Enneper's":[103],"surface,":[104],"under":[105],"appropriate":[106],"conditions.":[107],"Finally,":[108],"establish":[110],"exterior":[112],"analogue":[113],"Choe's":[115],"result":[116],"vertices.":[122]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-27T00:00:00"}