{"id":"https://openalex.org/W7221813656","doi":"https://doi.org/10.48550/arxiv.2610.18364","title":"Pseudolocality and strong uniqueness for complete Ricci flows","display_name":"Pseudolocality and strong uniqueness for complete Ricci flows","publication_year":2026,"publication_date":"2026-10-13","ids":{"openalex":"https://openalex.org/W7221813656","doi":"https://doi.org/10.48550/arxiv.2610.18364"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.18364","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.18364","pdf_url":"https://arxiv.org/pdf/2610.18364","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/2610.18364","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024082378","display_name":"Shaochuang Huang","orcid":"https://orcid.org/0000-0003-4148-3099","observed_orcids":["https://orcid.org/0000-0003-4148-3099"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huang, Shaochuang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5128557161","display_name":"Zhuo Peng","orcid":"https://orcid.org/0009-0006-0213-5373","observed_orcids":["https://orcid.org/0009-0006-0213-5373"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peng, Zhuo","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/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":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/ricci-flow","display_name":"Ricci flow","score":0.9670000076293945},{"id":"https://openalex.org/keywords/strong-uniqueness","display_name":"strong uniqueness","score":0.9710000157356262},{"id":"https://openalex.org/keywords/complete-riemannian-metrics","display_name":"complete Riemannian metrics","score":0.7799999713897705},{"id":"https://openalex.org/keywords/injectivity-radius","display_name":"injectivity radius","score":0.7789999842643738},{"id":"https://openalex.org/keywords/lower-ricci-curvature-bounds","display_name":"Ricci curvature lower bound","score":0.7509999871253967},{"id":"https://openalex.org/keywords/ricci-flat-metrics","display_name":"Ricci-flat metrics","score":0.9020000100135803},{"id":"https://openalex.org/keywords/flat-metrics","display_name":"flat metrics","score":0.9390000104904175},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.7549999952316284}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8535000085830688},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.8256000280380249},{"id":"https://openalex.org/C148729565","wikidata":"https://www.wikidata.org/wiki/Q1361396","display_name":"Ricci flow","level":4,"score":0.7785000205039978},{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.6947000026702881},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5827000141143799},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4839000105857849},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.48159998655319214},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.4684999883174896},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4041000008583069},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38909998536109924},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.38280001282691956},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3686000108718872},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.33230000734329224},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.3287000060081482},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.32350000739097595},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.31859999895095825},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.28299999237060547},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.2818000018596649},{"id":"https://openalex.org/C93361540","wikidata":"https://www.wikidata.org/wiki/Q848569","display_name":"Complete metric space","level":3,"score":0.2766999900341034},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.26829999685287476},{"id":"https://openalex.org/C2775918384","wikidata":"https://www.wikidata.org/wiki/Q4660961","display_name":"A priori estimate","level":2,"score":0.2628999948501587},{"id":"https://openalex.org/C127813850","wikidata":"https://www.wikidata.org/wiki/Q6803617","display_name":"Mean curvature flow","level":4,"score":0.2556000053882599}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.18364","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.18364","pdf_url":"https://arxiv.org/pdf/2610.18364","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.2610.18364","doi":"https://doi.org/10.48550/arxiv.2610.18364","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.18364","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:2610.18364","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.18364","pdf_url":"https://arxiv.org/pdf/2610.18364","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":[{"id":"https://openalex.org/F4320321160","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221813656.pdf","grobid_xml":"https://content.openalex.org/works/W7221813656.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1970564715","https://openalex.org/W2331165194","https://openalex.org/W3049383224","https://openalex.org/W3094243910","https://openalex.org/W4403808722","https://openalex.org/W4404949299","https://openalex.org/W4416613190","https://openalex.org/W7220937940"],"related_works":["https://openalex.org/W7117129243","https://openalex.org/W2963319380","https://openalex.org/W2137779943","https://openalex.org/W2090898225","https://openalex.org/W4416613190","https://openalex.org/W2527895868","https://openalex.org/W2138780223","https://openalex.org/W7006526911","https://openalex.org/W1621224838","https://openalex.org/W2076639547"],"abstract_inverted_index":{"In":[0,89],"this":[1],"paper,":[2],"we":[3,40,91],"prove":[4,60],"a":[5,28,38,50,68],"uniform":[6],"pseudolocality":[7],"theorem":[8],"for":[9,44,83],"smooth":[10,45,63],"complete":[11,46,51,64,69,85],"Ricci":[12,18,47,65,104],"flows":[13,48],"whose":[14],"initial":[15,87],"metrics":[16],"have":[17],"curvature":[19,30],"bounded":[20],"below":[21],"and":[22],"uniformly":[23,73],"positive":[24,74],"injectivity":[25,75],"radius.":[26],"No":[27],"priori":[29],"bound":[31],"is":[32,77],"assumed":[33],"on":[34,99],"the":[35,54,100],"flow.":[36],"As":[37],"consequence,":[39],"obtain":[41],"strong":[42,101],"uniqueness":[43,102],"from":[49,67,106],"metric":[52,71],"with":[53,72],"above":[55],"geometric":[56],"bounds.":[57],"We":[58],"also":[59],"that":[61],"every":[62,110],"flow":[66,105],"Ricci-flat":[70],"radius":[76],"stationary.":[78],"The":[79],"same":[80],"conclusion":[81],"holds":[82],"any":[84],"flat":[86],"metric.":[88],"particular,":[90],"give":[92],"an":[93],"affirmative":[94],"answer":[95],"to":[96],"Chen's":[97],"question":[98],"of":[103],"Euclidean":[107],"space":[108],"in":[109],"dimension.":[111]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-15T00:00:00"}
