Lower volume growth estimates for Self-shrinkers of mean curvature flow

TL;DR

This paper establishes that complete noncompact self-shrinkers in mean curvature flow must have at least linear volume growth, providing a Calabi-Yau type lower bound.

Contribution

It proves a new lower volume growth estimate for self-shrinkers, showing they cannot grow slower than linearly, which advances understanding of their geometric properties.

Findings

Complete noncompact properly immersed self-shrinkers have at least linear volume growth.

The result extends Calabi-Yau type volume estimates to self-shrinkers.

Provides geometric constraints on the structure of self-shrinkers.

Abstract

We obtain a Calabi-Yau type lower volume growth estimates for complete noncompact self-shrinkers of the mean curvature flow, more precisely, every complete noncompact properly immersed self-shrinker has at least linear volume growth.