{"title":"Mean curvature flow with pinched curvature integral","authors":"Yongheng Han","doi":"10.1016/j.difgeo.2025.102244","DOIUrl":null,"url":null,"abstract":"<div><div>If Σ is an <em>n</em>-dimensional noncompact self-shrinker and the second fundamental form of Σ is <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> integrable for <span><math><mi>p</mi><mo>≥</mo><mi>n</mi></math></span>, we show that Σ is asymptotic to a regular cone. We also prove long-time existence of the mean curvature flow starting from complete manifolds with bounded curvature and small total curvature.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"99 ","pages":"Article 102244"},"PeriodicalIF":0.7000,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Geometry and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0926224525000191","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
If Σ is an n-dimensional noncompact self-shrinker and the second fundamental form of Σ is integrable for , we show that Σ is asymptotic to a regular cone. We also prove long-time existence of the mean curvature flow starting from complete manifolds with bounded curvature and small total curvature.
期刊介绍：
Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
