黎曼乘积中具有规定接触角的非参数平均曲率流

Pub Date : 2020-07-08 DOI:10.1515/agms-2020-0132

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

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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。

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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.

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