Eigenvalue estimates on shrinkers

TL;DR

This paper establishes an eigenvalue estimate applicable to all properly embedded self-similar shrinkers in mean curvature flow, extending previous results to include noncompact cases.

Contribution

It generalizes earlier eigenvalue estimates to noncompact self-similar shrinkers in mean curvature flow.

Findings

Eigenvalue estimate valid for all properly embedded shrinkers

Extension of previous work to noncompact cases

Broader applicability in mean curvature flow analysis

Abstract

We prove an eigenvalue estimate which holds on every properly embedded self-similar shrinker for mean curvature flow. This generalizes earlier work of Ding and Xin to the noncompact case.