Abstract
Our target in this paper is given upper bounds for the first stability eigenvalue of closed (compact without boundary) surfaces in a 3-Riemannian manifold endowed with a smooth density function. As consequence, we deduce a topological constraint for the existence of closed stable surfaces in non-negatively curved spaces and a result of no existence of closed stable self-shrinkers of the mean curvature flow in \(\mathbb {R}^{3}\).
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The authors would like to thank the referee for very valuable comments and suggestions.
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The first author was partially supported by CNPq, FAPEAL and CAPES/Brazil and the second author was supported by CAPES/Brazil.
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Batista, M., Santos, J.I. Upper Bounds for the First Stability Eigenvalue of Surfaces in 3-Riemannian Manifolds. Potential Anal 49, 91–103 (2018). https://doi.org/10.1007/s11118-017-9649-3
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DOI: https://doi.org/10.1007/s11118-017-9649-3