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arXiv · 1503.06062

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

Márcio Batista·José I. Santos
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Abstract

Let $Σ$ 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 $Σ$ 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.

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Márcio Batista, José I. Santos. 2015-03-20. On the first stability eigenvalue of surfaces with constant weighted mean curvature. https://arxiv.org/abs/1503.06062

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