黎曼乘积中具有规定接触角的非参数平均曲率流

IF 0.9 3区数学 Q2 MATHEMATICS

Analysis and Geometry in Metric Spaces Pub Date : 2020-07-08 DOI:10.1515/agms-2020-0132

Jean-Baptiste Casteras, E. Heinonen, I. Holopainen, J. D. de Lira

{"title":"黎曼乘积中具有规定接触角的非参数平均曲率流","authors":"Jean-Baptiste Casteras, E. Heinonen, I. Holopainen, J. D. de Lira","doi":"10.1515/agms-2020-0132","DOIUrl":null,"url":null,"abstract":"Abstract Assuming that there exists a translating soliton u∞ with speed C in a domain Ω and with prescribed contact angle on ∂Ω, we prove that a graphical solution to the mean curvature flow with the same prescribed contact angle converges to u∞ + Ct as t →∞. We also generalize the recent existence result of Gao, Ma, Wang and Weng to non-Euclidean settings under suitable bounds on convexity of Ω and Ricci curvature in Ω.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2020-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Non-Parametric Mean Curvature Flow with Prescribed Contact Angle in Riemannian Products\",\"authors\":\"Jean-Baptiste Casteras, E. Heinonen, I. Holopainen, J. D. de Lira\",\"doi\":\"10.1515/agms-2020-0132\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Assuming that there exists a translating soliton u∞ with speed C in a domain Ω and with prescribed contact angle on ∂Ω, we prove that a graphical solution to the mean curvature flow with the same prescribed contact angle converges to u∞ + Ct as t →∞. We also generalize the recent existence result of Gao, Ma, Wang and Weng to non-Euclidean settings under suitable bounds on convexity of Ω and Ricci curvature in Ω.\",\"PeriodicalId\":48637,\"journal\":{\"name\":\"Analysis and Geometry in Metric Spaces\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2020-07-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Analysis and Geometry in Metric Spaces\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/agms-2020-0132\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis and Geometry in Metric Spaces","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/agms-2020-0132","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

摘要:假设在Ω域中存在一个速度为C的平移孤子u∞，并且在∂Ω上具有规定的接触角，证明了具有相同规定接触角的平均曲率流的图形解收敛于u∞+ Ct，使t→∞。我们还将Gao, Ma, Wang和Weng最近的存在性结果推广到Ω和Ω中Ricci曲率在合适的凸性边界下的非欧几里德集合。

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

Non-Parametric Mean Curvature Flow with Prescribed Contact Angle in Riemannian Products

Abstract Assuming that there exists a translating soliton u∞ with speed C in a domain Ω and with prescribed contact angle on ∂Ω, we prove that a graphical solution to the mean curvature flow with the same prescribed contact angle converges to u∞ + Ct as t →∞. We also generalize the recent existence result of Gao, Ma, Wang and Weng to non-Euclidean settings under suitable bounds on convexity of Ω and Ricci curvature in Ω.

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

Analysis and Geometry in Metric Spaces Mathematics-Geometry and Topology

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Analysis and Geometry in Metric Spaces is an open access electronic journal that publishes cutting-edge research on analytical and geometrical problems in metric spaces and applications. We strive to present a forum where all aspects of these problems can be discussed. AGMS is devoted to the publication of results on these and related topics: Geometric inequalities in metric spaces, Geometric measure theory and variational problems in metric spaces, Analytic and geometric problems in metric measure spaces, probability spaces, and manifolds with density, Analytic and geometric problems in sub-riemannian manifolds, Carnot groups, and pseudo-hermitian manifolds. Geometric control theory, Curvature in metric and length spaces, Geometric group theory, Harmonic Analysis. Potential theory, Mass transportation problems, Quasiconformal and quasiregular mappings. Quasiconformal geometry, PDEs associated to analytic and geometric problems in metric spaces.