Gradient estimates and lower bound for the blow-up time of star-shaped mean curvature flow

TL;DR

This paper provides a new proof of gradient estimates for star-shaped mean curvature flow without convexity assumptions and establishes a lower bound for the blow-up time.

Contribution

It introduces a novel proof technique for gradient estimates and derives a lower bound for the blow-up time in star-shaped mean curvature flow.

Findings

Gradient estimate valid for short time without convexity

Lower bound for blow-up time established

Proof method applicable to star-shaped hypersurfaces

Abstract

In this paper we consider a star-shaped hypersurface flow by mean curvature. Without any assumption on the convexity, we give a new proof of gradient estimate for a short time. As an application, we also give a lower bound for the blowing up time.