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

Liangjun Weng

Vol. 308 (2020), No. 2, 435–472

DOI: 10.2140/pjm.2020.308.435

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