Non-Parametric Mean Curvature Flow with Prescribed Contact Angle in Riemannian Products-Reference-Cited by-同舟云学术

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

Published:2022-01-01 Issue:1 Volume:10 Page:31-39
ISSN:2299-3274
Container-title:Analysis and Geometry in Metric Spaces
language:en
Short-container-title:

Author:

Casteras Jean-Baptiste¹,Heinonen Esko²,Holopainen Ilkka¹,De Lira Jorge H.³

Affiliation:

1. Department of Mathematics and Statistics , University of Helsinki , Helsinki , Finland

2. Department of Mathematics and Statistics , University of Jyväskylä , Jyväskylä , Finland

3. Departamento de Matemática , Universidade Federal do Ceará , Fortaleza, Ceará , Brazil

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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Geometry and Topology,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/agms-2020-0132/pdf

Reference8 articles.

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