Geometric properties of self-shrinkers in cylinder shrinking Ricci solitons

2016/09/12 by Matheus Vieira, Vieira, Matheus, Detang Zhou +1 · 1 citation
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Advanced Differential Geometry Research

paper · pdf · doi:10.48550/arxiv.1609.03247

Abstract

In this paper we prove some spectral properties of the drifted Laplacian of self-shrinkers properly immersed in gradient shrinking Ricci solitons. Then we use these results to prove some geometric properties of self-shrinkers. For example, we describe a collection of domains in the ambient space that cannot contain self-shrinkers.

Cited by

• An eigenvalue estimate for self-shrinkers in a Ricci shirinker

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