Sharp estimates for mean curvature flow of graphs

TL;DR

This paper provides precise estimates for the evolution of graphs under mean curvature flow, improving upon previous non-sharp bounds and illustrating their optimality with examples.

Contribution

It introduces sharp estimates for mean curvature flow of graphs, advancing the accuracy of prior bounds by Ecker and Huisken.

Findings

Establishment of sharp bounds for mean curvature flow

Examples demonstrating the sharpness of these estimates

Improved understanding of the flow's behavior

Abstract

Sharp estimates for mean curvature flow of graphs are shown and examples are given to illustrate why these are sharp. The estimates improves earlier (non-sharp) estimates of Klaus Ecker and Gerhard Huisken.