Mean Curvature Flows of Graphs with Neumann Boundary condition

Abstract

In this paper, we study the mean curvature flow of graphs with Neumann boundary condition. The main aim is to use the maximum principle to get the boundary gradient estimate for solutions. In particular, we obtain the corresponding existence theorem for the mean curvature flow of graphs.

11pages. This is an extended parabolic version of arxiv:1406.0046(published in Adv.Math.290(2016),1010-1039.)