Well-posedness of mean curvature flow

TL;DR

This paper provides a new proof for the existence and uniqueness of mean curvature flow starting from hypersurfaces with bounded second fundamental form, emphasizing continuous dependence on initial data.

Contribution

It introduces a novel proof technique using heat kernel estimates and contraction mapping for mean curvature flow with bounded second fundamental form.

Findings

Existence and uniqueness of mean curvature flow established

Flow depends continuously on initial hypersurface data

New proof approach using heat kernel estimates

Abstract

In this paper, using heat kernel estimates and contraction mapping principle, we give a new proof of the existence and uniqueness of mean curvature flow starting from hypersurface with bounded second fundamental form. Moreover, we show the continuous dependence of mean curvature flow on initial data.