{"title":"Existence of 5 minimal tori in 3-spheres of positive Ricci curvature","authors":"Adrian Chun-Pong Chu, Yangyang Li","doi":"arxiv-2409.09315","DOIUrl":null,"url":null,"abstract":"In 1989, B. White conjectured that every Riemannian 3-sphere has at least 5\nembedded minimal tori. We confirm this conjecture for 3-spheres of positive\nRicci curvature. While our proof uses min-max theory, the underlying heuristics\nare largely inspired by mean curvature flow.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"3 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Geometric Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09315","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In 1989, B. White conjectured that every Riemannian 3-sphere has at least 5
embedded minimal tori. We confirm this conjecture for 3-spheres of positive
Ricci curvature. While our proof uses min-max theory, the underlying heuristics
are largely inspired by mean curvature flow.
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