Vol. 308, No. 2, 2020

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Mean curvature flow in a Riemannian manifold endowed with a Killing vector field

Liangjun Weng

Vol. 308 (2020), No. 2, 435–472
Abstract

We consider the Killing graphs over a bounded regular domain M in an integral distribution orthogonal to a Killing vector field with prescribed variable contact angle. Under some appropriate condition between the geometry of the domain and the contact angle, based on the maximum principle and the approximation method, we show that the solutions to the mean curvature flow of Killing graphs with capillarity type boundary condition converge to a translating solution.

Keywords
Killing vector field, warped product manifold, mean curvature flow, uniform gradient estimate, variable contact angle
Mathematical Subject Classification 2010
Primary: 53C44
Secondary: 35J66
Milestones
Received: 14 June 2019
Revised: 12 December 2019
Accepted: 25 July 2020
Published: 9 December 2020
Authors
Liangjun Weng
School of Mathematical Sciences
Shanghai Jiao Tong University
Shanghai
China