A local noncollapsing estimate for mean curvature flow

TL;DR

This paper establishes a local noncollapsing estimate for mean curvature flow, which, combined with previous work, implies that certain ancient convex solutions are noncollapsed, advancing understanding of geometric flow behavior.

Contribution

The authors prove a local noncollapsing estimate for mean curvature flow, extending previous global results to a local setting.

Findings

Established a local noncollapsing estimate for mean curvature flow.

Showed that certain ancient convex solutions are noncollapsed.

Connected local estimates with global properties of ancient solutions.

Abstract

We prove a local version of the noncollapsing estimate for mean curvature flow. By combining our result with earlier work of X.-J. Wang, it follows that certain ancient convex solutions that sweep out the entire space are noncollapsed.