{"id":"https://openalex.org/W7212035593","doi":"https://doi.org/10.48550/arxiv.2609.06910","title":"Minimal Two-Spheres and Manifolds with Positive Isotropic Curvature","display_name":"Minimal Two-Spheres and Manifolds with Positive Isotropic Curvature","publication_year":2026,"publication_date":"2026-09-07","ids":{"openalex":"https://openalex.org/W7212035593","doi":"https://doi.org/10.48550/arxiv.2609.06910"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.06910","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.06910","pdf_url":"https://arxiv.org/pdf/2609.06910","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/2609.06910","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089478132","display_name":"Tsz-Kiu Aaron Chow","orcid":"https://orcid.org/0000-0002-3072-5104","observed_orcids":["https://orcid.org/0000-0002-3072-5104"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chow, Tsz-Kiu Aaron","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5151993227","display_name":"Yipeng Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]},{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["HK","US"],"is_corresponding":false,"raw_author_name":"Wang, Yipeng","raw_affiliation_strings":["Department of Mathematics , Hong Kong University of Science and Tech- nology , Hong Kong S.A .R. , China","Department of Mathematics , Princeton University , Princeton , NJ 08544 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Hong Kong University of Science and Tech- nology , Hong Kong S.A .R. , China","institution_ids":["https://openalex.org/I200769079"]},{"raw_affiliation_string":"Department of Mathematics , Princeton University , Princeton , NJ 08544 , USA","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":4,"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":0.948199987411499,"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":0.948199987411499,"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":0.04100000113248825,"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":0.004699999932199717,"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/diffeomorphism-classification","display_name":"diffeomorphism classification","score":0.8970000147819519},{"id":"https://openalex.org/keywords/closed-manifolds","display_name":"closed manifolds","score":0.8889999985694885}],"concepts":[{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.7767999768257141},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.7470999956130981},{"id":"https://openalex.org/C47556283","wikidata":"https://www.wikidata.org/wiki/Q1058314","display_name":"Diffeomorphism","level":2,"score":0.6960999965667725},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5979999899864197},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.578499972820282},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.43790000677108765},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3961000144481659},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.38280001282691956},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.36640000343322754},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.32109999656677246},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31029999256134033},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.30970001220703125},{"id":"https://openalex.org/C2983854663","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Negative curvature","level":3,"score":0.3037000000476837},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2935999929904938},{"id":"https://openalex.org/C42448751","wikidata":"https://www.wikidata.org/wiki/Q855622","display_name":"Sectional curvature","level":4,"score":0.2858999967575073},{"id":"https://openalex.org/C84985374","wikidata":"https://www.wikidata.org/wiki/Q1892644","display_name":"Torsion of a curve","level":5,"score":0.2700999975204468},{"id":"https://openalex.org/C16977076","wikidata":"https://www.wikidata.org/wiki/Q1589551","display_name":"Principal curvature","level":4,"score":0.2565000057220459},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.25049999356269836}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.06910","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.06910","pdf_url":"https://arxiv.org/pdf/2609.06910","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.2609.06910","doi":"https://doi.org/10.48550/arxiv.2609.06910","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.06910","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:2609.06910","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.06910","pdf_url":"https://arxiv.org/pdf/2609.06910","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/W7212035593.pdf","grobid_xml":"https://content.openalex.org/works/W7212035593.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W4378771257","https://openalex.org/W4404317927","https://openalex.org/W7204600036"],"related_works":["https://openalex.org/W1972386875","https://openalex.org/W1964697829","https://openalex.org/W4378771257","https://openalex.org/W4389116420","https://openalex.org/W2463544790","https://openalex.org/W838498658","https://openalex.org/W3008290829","https://openalex.org/W2976200038","https://openalex.org/W2158350859","https://openalex.org/W2185099954"],"abstract_inverted_index":{"We":[0],"improve":[1],"the":[2,16,26,37],"Micallef--Moore":[3],"index":[4],"estimate":[5],"for":[6],"harmonic":[7],"two-spheres":[8],"in":[9,36],"$n$-manifolds":[10],"with":[11,21,32],"positive":[12,33],"isotropic":[13,34],"curvature":[14,35],"to":[15],"sharp":[17],"bound":[18],"$n-3$.":[19],"Combining":[20],"recent":[22],"work,":[23],"this":[24],"completes":[25],"diffeomorphism":[27],"classification":[28],"of":[29],"closed":[30],"manifolds":[31],"remaining":[38],"dimensions":[39],"five":[40],"and":[41],"six.":[42]},"counts_by_year":[{"year":2026,"cited_by_count":4}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-10T00:00:00"}
