{"id":"https://openalex.org/W4221143412","doi":"https://doi.org/10.2140/gt.2026.30.1277","title":"Closed Ricci flows with singularities modeled on asymptotically conical shrinkers","display_name":"Closed Ricci flows with singularities modeled on asymptotically conical shrinkers","publication_year":2026,"publication_date":"2026-07-09","ids":{"openalex":"https://openalex.org/W4221143412","doi":"https://doi.org/10.2140/gt.2026.30.1277"},"language":"en","primary_location":{"id":"doi:10.2140/gt.2026.30.1277","doi":"https://doi.org/10.2140/gt.2026.30.1277","is_oa":true,"landing_page_url":"https://doi.org/10.2140/gt.2026.30.1277","pdf_url":"https://msp.org/gt/2026/30-4/gt-v30-n4-p02-s.pdf","source":{"id":"https://openalex.org/S50220091","display_name":"Geometry & Topology","issn_l":"1364-0380","issn":["1364-0380","1465-3060"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320446","host_organization_name":"Mathematical Sciences Publishers","host_organization_lineage":["https://openalex.org/P4310320446"],"host_organization_lineage_names":["Mathematical Sciences Publishers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Geometry & Topology","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://msp.org/gt/2026/30-4/gt-v30-n4-p02-s.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062575485","display_name":"Maxwell Stolarski","orcid":"https://orcid.org/0009-0002-1544-3827","observed_orcids":["https://orcid.org/0009-0002-1544-3827"]},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Maxwell Stolarski","raw_affiliation_strings":["Warwick Mathematics Institute, University of Warwick, Coventry, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Warwick Mathematics Institute, University of Warwick, Coventry, United Kingdom","institution_ids":["https://openalex.org/I39555362"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5062575485"],"corresponding_institution_ids":["https://openalex.org/I39555362"],"apc_list":null,"apc_paid":null,"fwci":3.9001,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.85060118,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"30","issue":"4","first_page":"1277","last_page":"1370"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9994999766349792,"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":0.9994999766349792,"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/T12351","display_name":"Geometry and complex manifolds","score":0.00019999999494757503,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.0,"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/ricci-flow","display_name":"Ricci flow","score":0.9599999785423279},{"id":"https://openalex.org/keywords/singularity-formation","display_name":"singularity formation","score":0.6589999794960022},{"id":"https://openalex.org/keywords/closed-manifolds","display_name":"closed manifolds","score":0.949999988079071},{"id":"https://openalex.org/keywords/blow-up","display_name":"blow-up","score":0.9449999928474426},{"id":"https://openalex.org/keywords/harmonic-map-heat-flow","display_name":"harmonic map heat flow","score":0.8740000128746033},{"id":"https://openalex.org/keywords/holder-estimates","display_name":"H\u00f6lder estimates","score":0.7279999852180481}],"concepts":[{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.801626443862915},{"id":"https://openalex.org/C124961601","wikidata":"https://www.wikidata.org/wiki/Q2518149","display_name":"Conical surface","level":2,"score":0.7966862916946411},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.7861626148223877},{"id":"https://openalex.org/C148729565","wikidata":"https://www.wikidata.org/wiki/Q1361396","display_name":"Ricci flow","level":4,"score":0.6769400835037231},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6657516360282898},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.526861310005188},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4819369316101074},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.4750613868236542},{"id":"https://openalex.org/C87651913","wikidata":"https://www.wikidata.org/wiki/Q464949","display_name":"Soliton","level":3,"score":0.4397985637187958},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4349079728126526},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3311121463775635},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24281546473503113},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20087456703186035},{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.16595208644866943},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1294756531715393},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.2140/gt.2026.30.1277","doi":"https://doi.org/10.2140/gt.2026.30.1277","is_oa":true,"landing_page_url":"https://doi.org/10.2140/gt.2026.30.1277","pdf_url":"https://msp.org/gt/2026/30-4/gt-v30-n4-p02-s.pdf","source":{"id":"https://openalex.org/S50220091","display_name":"Geometry & Topology","issn_l":"1364-0380","issn":["1364-0380","1465-3060"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320446","host_organization_name":"Mathematical Sciences Publishers","host_organization_lineage":["https://openalex.org/P4310320446"],"host_organization_lineage_names":["Mathematical Sciences Publishers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Geometry & Topology","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2202.03386","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2202.03386","pdf_url":"https://arxiv.org/pdf/2202.03386","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:wrap.warwick.ac.uk:196248","doi":null,"is_oa":true,"landing_page_url":"https://wrap.warwick.ac.uk/id/eprint/196248/1/maths-020226-wrap-acsingularities_v3.pdf","pdf_url":"https://wrap.warwick.ac.uk/id/eprint/196248/7/gt-v30-n4-p02-s.pdf","source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"},{"id":"doi:10.48550/arxiv.2202.03386","doi":"https://doi.org/10.48550/arxiv.2202.03386","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2202.03386","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":"doi:10.2140/gt.2026.30.1277","doi":"https://doi.org/10.2140/gt.2026.30.1277","is_oa":true,"landing_page_url":"https://doi.org/10.2140/gt.2026.30.1277","pdf_url":"https://msp.org/gt/2026/30-4/gt-v30-n4-p02-s.pdf","source":{"id":"https://openalex.org/S50220091","display_name":"Geometry & Topology","issn_l":"1364-0380","issn":["1364-0380","1465-3060"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320446","host_organization_name":"Mathematical Sciences Publishers","host_organization_lineage":["https://openalex.org/P4310320446"],"host_organization_lineage_names":["Mathematical Sciences Publishers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Geometry & Topology","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4779579228","display_name":null,"funder_award_id":"ECF-2023-182","funder_id":"https://openalex.org/F4320319993","funder_display_name":"Leverhulme Trust"}],"funders":[{"id":"https://openalex.org/F4320319993","display_name":"Leverhulme Trust","ror":"https://ror.org/012mzw131"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4221143412.pdf","grobid_xml":"https://content.openalex.org/works/W4221143412.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4412846044","https://openalex.org/W2962948898","https://openalex.org/W7052793065","https://openalex.org/W2964078945","https://openalex.org/W11768205","https://openalex.org/W2843775189","https://openalex.org/W7128548575","https://openalex.org/W2964131001","https://openalex.org/W2893343519","https://openalex.org/W3081222598"],"abstract_inverted_index":{"Given":[0],"an":[1],"asymptotically":[2],"conical,":[3],"shrinking,":[4],"gradient":[5],"Ricci":[6,14],"soliton,":[7],"we":[8],"show":[9],"that":[10,21],"there":[11],"exists":[12],"a":[13,18,23,42],"flow":[15,110],"solution":[16],"on":[17,27,35,54],"closed":[19],"manifold":[20],"forms":[22],"finite-time":[24],"singularity":[25,48],"modeled":[26],"the":[28,36,47,61],"given":[29],"soliton.No":[30],"symmetry":[31],"or":[32],"K\u00e4hler":[33],"assumptions":[34],"soliton":[37],"are":[38],"required.The":[39],"proof":[40,62],"provides":[41],"precise":[43],"asymptotic":[44],"description":[45],"of":[46,60,63,78,85,95],"formation.1.":[49],"Introduction":[50],"1277":[51],"2.":[52],"Preliminaries":[53],"shrinking":[55],"solitons":[56],"1280":[57],"3.":[58],"Strategy":[59],"Theorem":[64,96],"1.1":[65,97],"1292":[66],"4.":[67],"Setup":[68],"1294":[69],"5.":[70],"Preliminary":[71],"estimates":[72,115],"1307":[73],"6.":[74],"Preservation":[75],"and":[76],"improvement":[77],"C":[79],"2":[80,87],"bounds":[81],"1312":[82],"7.":[83],"Behavior":[84],"L":[86],"f":[88],".M":[89],"/":[90],"quantities":[91],"1333":[92],"8.":[93],"Proof":[94],"1336":[98],"Appendix":[99,105,112,120],"A.":[100],"Rounding":[101],"out":[102],"cones":[103],"1350":[104],"B.":[106],"Harmonic":[107],"map":[108],"heat":[109],"1358":[111],"C.":[113],"H\u00f6lder":[114],"in":[116],"Euclidean":[117],"space":[118],"1364":[119],"D.":[121]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2022-04-03T00:00:00"}