正利玛窦曲率的 3 球体中存在 5 个最小转矩

arXiv - MATH - Geometric Topology Pub Date : 2024-09-14 DOI:arxiv-2409.09315

Adrian Chun-Pong Chu, Yangyang Li

{"title":"正利玛窦曲率的 3 球体中存在 5 个最小转矩","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":"{\"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}","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

摘要

1989 年，B. 怀特猜想每个黎曼 3 球至少有 5 个嵌入的最小环。我们对具有正里奇曲率的 3 球体证实了这一猜想。虽然我们的证明使用了最小最大理论，但其基本启发式主要来自平均曲率流。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Existence of 5 minimal tori in 3-spheres of positive Ricci curvature

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv - MATH - Geometric Topology

自引率

0.00%

发文量