{"id":"https://openalex.org/W7204912977","doi":"https://doi.org/10.48550/arxiv.2608.29853","title":"Sharp monotonicity for closed three-manifolds with positive scalar curvature","display_name":"Sharp monotonicity for closed three-manifolds with positive scalar curvature","publication_year":2026,"publication_date":"2026-08-30","ids":{"openalex":"https://openalex.org/W7204912977","doi":"https://doi.org/10.48550/arxiv.2608.29853"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.29853","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29853","pdf_url":"https://arxiv.org/pdf/2608.29853","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/2608.29853","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120756106","display_name":"Cosmin Manea","orcid":"https://orcid.org/0009-0004-1940-1215","observed_orcids":["https://orcid.org/0009-0004-1940-1215"]},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Manea, Cosmin","raw_affiliation_strings":["Department of Mathematics , Massachusetts Institute of Technology , 77 Massachusetts Avenue , Cambridge , MA , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Massachusetts Institute of Technology , 77 Massachusetts Avenue , Cambridge , MA , USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5120756106"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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":0.9970999956130981,"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":0.9970999956130981,"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":0.0013000000035390258,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.00039999998989515007,"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/positive-scalar-curvature","display_name":"positive scalar curvature","score":1.0},{"id":"https://openalex.org/keywords/green-s-function","display_name":"Green's function","score":0.9539999961853027},{"id":"https://openalex.org/keywords/enclosed-mass","display_name":"enclosed mass","score":0.8289999961853027},{"id":"https://openalex.org/keywords/sublevel-sets","display_name":"sublevel sets","score":0.8489999771118164},{"id":"https://openalex.org/keywords/ricci-flow","display_name":"Ricci flow","score":0.46299999952316284}],"concepts":[{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.8690999746322632},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7366999983787537},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5953999757766724},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5564000010490417},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5324000120162964},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43380001187324524},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3686000108718872},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.3513000011444092},{"id":"https://openalex.org/C110521144","wikidata":"https://www.wikidata.org/wiki/Q193460","display_name":"Scalar field","level":2,"score":0.28999999165534973},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.24140000343322754}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.29853","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29853","pdf_url":"https://arxiv.org/pdf/2608.29853","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.2608.29853","doi":"https://doi.org/10.48550/arxiv.2608.29853","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.29853","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:2608.29853","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29853","pdf_url":"https://arxiv.org/pdf/2608.29853","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204912977.pdf","grobid_xml":"https://content.openalex.org/works/W7204912977.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W4407012837","https://openalex.org/W4417127469","https://openalex.org/W4417142922","https://openalex.org/W7111028845","https://openalex.org/W7128814327","https://openalex.org/W7133313734","https://openalex.org/W7167666717"],"related_works":["https://openalex.org/W4392110475","https://openalex.org/W4417142922","https://openalex.org/W4391985713","https://openalex.org/W7167666717","https://openalex.org/W2040152921","https://openalex.org/W2949092749","https://openalex.org/W3164343096","https://openalex.org/W3212410705","https://openalex.org/W7215109697","https://openalex.org/W2150897356"],"abstract_inverted_index":{"We":[0,28],"prove":[1],"two":[2],"sharp":[3],"monotonicity":[4,39],"formulae":[5],"for":[6,24],"the":[7,21,38,47,54,59],"natural":[8],"Green's":[9,51],"function":[10,52],"of":[11,40,46,50,58],"a":[12,41],"closed":[13],"three-manifold":[14],"with":[15],"positive":[16],"scalar":[17,26],"curvature,":[18],"analogous":[19],"to":[20],"Munteanu-Wang":[22],"theorem":[23],"non-negative":[25],"curvature.":[27],"also":[29],"show":[30],"that":[31],"both":[32],"results":[33],"may":[34],"be":[35],"interpreted":[36],"as":[37],"suitably":[42],"defined":[43],"\"enclosed":[44],"mass\"":[45],"sublevel":[48],"sets":[49],"in":[53],"corresponding":[55],"\"conformal\"":[56],"blow-up":[57],"manifold.":[60]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}
