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

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.

arXiv comment14 pages, we change the title of the paper, delete a theorem about Ricci soliton which has been proved by Ovidiu Munteanu and Jiaping Wang, and correct a gap in the proof of our theorem in the previous version