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

2011/12/05 by Haizhong Li, Yong Wei, Li, Haizhong +1
Mathematics · #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1112.0828

openalex publication_date 2011/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

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• An unknottedness result for noncompact self shrinkers
• Classification and rigidity of self-shrinkers in the Mean curvature flow
• Volume estimate about shrinkers
• On the rate of convergence of the rescaled mean curvature flow