Volume estimate about shrinkers

Details Volume estimate about shrinkers Volume estimate about shrinkers

2011-06-24

arxiv.org/abs/1106.4950v1

Mathematics

Differential Geometry

Scientific paper

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.

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