On the first stability eigenvalue of surfaces with constant weighted mean curvature

Márcio Batista; José I. Santos

On the first stability eigenvalue of surfaces with constant weighted mean curvature

Differential Geometry 2015-03-23 v1

Authors: Márcio Batista , José I. Santos

Abstract

Let $\Sigma$ be a compact immersed surface with constant weighted mean curvature $H_f$ in a weighted manifold $(M^3,g,f)$ . In this paper we obtain upper bounds for the first eigenvalue of the weighted Jacobi operator on $\Sigma$ in terms of $H_f$ and the curvature of the ambient. As consequence we obtain that there is no stable self-shrinker of the mean curvature flow.

Keywords

constant weighted mean curvature first stability eigenvalue weighted Jacobi operator weighted manifold self-shrinker mean curvature flow

Cite

@article{arxiv.1503.06062,
  title  = {On the first stability eigenvalue of surfaces with constant weighted mean curvature},
  author = {Márcio Batista and José I. Santos},
  journal= {arXiv preprint arXiv:1503.06062},
  year   = {2015}
}

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12 pages

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