Volume estimate about shrinkers

Abstract

We derive a precise estimate on the volume growth of the level set of a potential function on a complete noncompact Riemannian manifold. As applications, we obtain the volume growth rate of a complete noncompact self-shrinker and a gradient shrinking Ricci soliton. We also prove the equivalence of weighted volume finiteness, polynomial volume growth and properness of an immersed self-shrinker in Euclidean space.

References are updated

References in corpus (3)

• Generic mean curvature flow I; generic singularities
• Volume growth, eigenvalue and compactness for self-shrinkers
• Smooth compactness of self-shrinkers

Cited by in corpus (4)

• On a classification theorem for self-shrinkers
• The Rigidity Theorems of Self Shrinkers via Gauss maps
• Complete self-shrinkers of the mean curvature flow
• Some results on space-like self-shrinkers