Modified mean curvature flow of graphs in Riemannian manifolds

TL;DR

This paper establishes a priori estimates and proves the existence of smooth, long-term solutions for a modified mean curvature flow of graphs in Riemannian manifolds with a Killing vector field.

Contribution

It introduces a modified mean curvature flow in Riemannian manifolds and proves existence and estimates for solutions, extending previous results to this new setting.

Findings

Height, gradient, and curvature estimates are obtained.

Existence of smooth, entire, long-time solutions is proven.

The flow is studied in the context of manifolds with Killing vector fields.

Abstract

We obtain height, gradient, and curvature a priori estimates for a modified mean curvature flow in Riemannian manifolds endowed with a Killing vector field. As a consequence, we prove the existence of smooth, entire, longtime solutions for this extrinsic flow with smooth initial data.