Mean curvature flow of Killing graphs

TL;DR

This paper investigates the evolution of graphs under mean curvature flow in Riemannian manifolds with a Killing vector field, showing convergence to a minimal graph touching a cylinder orthogonally at the boundary.

Contribution

It introduces a new analysis of mean curvature flow for Killing graphs and proves convergence to a minimal graph with boundary contact conditions.

Findings

Graphs converge to a bounded minimal graph

The minimal graph contacts the cylinder orthogonally at the boundary

Results apply to specific cases of mean curvature flow in Riemannian manifolds

Abstract

We study a Neumann problem related to the evolution of graphs under mean curvature flow in Riemannian manifolds endowed with a Killing vector field. We prove that in a particular case these graphs converge to a bounded minimal graph which contacts the cylinder over the domain orthogonally along its boundary.