{"id":"https://openalex.org/W7221521292","doi":"https://doi.org/10.48550/arxiv.2610.13848","title":"A counterexample to Nirenberg's conjecture on closed asymptotic curves","display_name":"A counterexample to Nirenberg's conjecture on closed asymptotic curves","publication_year":2026,"publication_date":"2026-10-09","ids":{"openalex":"https://openalex.org/W7221521292","doi":"https://doi.org/10.48550/arxiv.2610.13848"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.13848","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.13848","pdf_url":"https://arxiv.org/pdf/2610.13848","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/2610.13848","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035857841","display_name":"Harrison Banks","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Banks, Harrison","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019994337","display_name":"Mohammad Ghomi","orcid":"https://orcid.org/0000-0003-3767-9347","observed_orcids":["https://orcid.org/0000-0003-3767-9347"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ghomi, Mohammad","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5120743563","display_name":"Hongda Qiu","orcid":"https://orcid.org/0000-0002-9681-5620","observed_orcids":["https://orcid.org/0000-0002-9681-5620"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qiu, Hongda","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5040522504","display_name":"Matteo Raffaelli","orcid":"https://orcid.org/0000-0002-4908-196X","observed_orcids":["https://orcid.org/0000-0002-4908-196X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Raffaelli, Matteo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.6147000193595886,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.6147000193595886,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.37700000405311584,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.0017000000225380063,"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/asymptotic-curves","display_name":"asymptotic curves","score":0.7979999780654907},{"id":"https://openalex.org/keywords/ruled-surfaces","display_name":"ruled surfaces","score":0.9089999794960022},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.8989999890327454},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.6710000038146973},{"id":"https://openalex.org/keywords/differential-geometry-of-surfaces","display_name":"differential geometry of surfaces","score":0.7129999995231628}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.836899995803833},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.763700008392334},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.635699987411499},{"id":"https://openalex.org/C70251129","wikidata":"https://www.wikidata.org/wiki/Q260928","display_name":"Jordan curve theorem","level":2,"score":0.5591999888420105},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.5501000285148621},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5479999780654907},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5248000025749207},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.41830000281333923},{"id":"https://openalex.org/C58315980","wikidata":"https://www.wikidata.org/wiki/Q179436","display_name":"Asymptote","level":2,"score":0.41519999504089355},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.40720000863075256},{"id":"https://openalex.org/C40890689","wikidata":"https://www.wikidata.org/wiki/Q2166240","display_name":"Osculating circle","level":2,"score":0.40220001339912415},{"id":"https://openalex.org/C24209939","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic formula","level":2,"score":0.3569999933242798},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.322299987077713},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.2815000116825104},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.26820001006126404},{"id":"https://openalex.org/C161223928","wikidata":"https://www.wikidata.org/wiki/Q3775868","display_name":"Center of curvature","level":4,"score":0.26600000262260437},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.2651999890804291},{"id":"https://openalex.org/C47890412","wikidata":"https://www.wikidata.org/wiki/Q1179296","display_name":"Tangent vector","level":3,"score":0.260699987411499},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2583000063896179},{"id":"https://openalex.org/C205147927","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic analysis","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.13848","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.13848","pdf_url":"https://arxiv.org/pdf/2610.13848","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.2610.13848","doi":"https://doi.org/10.48550/arxiv.2610.13848","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.13848","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:2610.13848","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.13848","pdf_url":"https://arxiv.org/pdf/2610.13848","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/W7221521292.pdf","grobid_xml":"https://content.openalex.org/works/W7221521292.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W7166646277","https://openalex.org/W7220959588"],"related_works":["https://openalex.org/W7220959588","https://openalex.org/W4415011028","https://openalex.org/W1987713853","https://openalex.org/W1504361705","https://openalex.org/W7100417891","https://openalex.org/W2023360351","https://openalex.org/W7223276387","https://openalex.org/W7166646277","https://openalex.org/W1592821550","https://openalex.org/W2014172430"],"abstract_inverted_index":{"We":[0],"construct":[1],"a":[2,37,40,54,66,76,80],"smooth":[3],"embedded":[4],"annulus":[5],"in":[6,13,23],"Euclidean":[7],"3-space":[8],"with":[9],"negative":[10],"Gauss":[11],"curvature":[12],"its":[14],"interior":[15],"whose":[16],"boundary":[17],"consists":[18],"of":[19,43,79],"strictly":[20],"convex":[21],"curves":[22],"planes":[24],"tangent":[25],"to":[26,39],"the":[27],"annulus,":[28],"and":[29],"which":[30,52],"contains":[31],"closed":[32,55],"asymptotic":[33,63,71],"curves.":[34],"This":[35],"gives":[36],"counterexample":[38],"1962":[41],"conjecture":[42],"Nirenberg.":[44],"The":[45,69],"construction":[46],"is":[47,58,73],"based":[48],"on":[49,65],"Lelieuvre's":[50],"formula,":[51],"yields":[53],"curve":[56,64,72],"that":[57],"then":[59],"realized":[60],"as":[61],"an":[62],"ruled":[67],"annulus.":[68],"second":[70],"obtained":[74],"from":[75],"periodic":[77],"solution":[78],"Riccati":[81],"equation.":[82]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-10-13T00:00:00"}