Eigenvalue estimates for the stability operator of CMC compact surfaces in three-dimensional warped products

DOI10.1016/j.jmaa.2015.10.016zbMath1328.53075OpenAlexW1776212660MaRDI QIDQ891435

Irene Ortiz, Miguel Angel Meroño

Publication date: 17 November 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2015.10.016

zbMATH Keywords

surfaceconstant mean curvaturewarped productstability eigenvalue

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

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Sharp eigenvalue estimates of closed $H$-hypersurfaces in locally symmetric spaces

Cites Work

• First stability eigenvalue characterization of CMC Hopf tori into Riemannian Killing submersions
• New characterizations of the Clifford tori and the Veronese surface
• Existence of prescribed mean curvature graphs in hyperbolic space
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• Stable constant mean curvature hypersurfaces in some Riemannian manifolds
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• Minimal varieties in Riemannian manifolds
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• First stability eigenvalue characterization of Clifford hypersurfaces
• A spectral characterization of the $H(r)$-torus by the first stability eigenvalue
• CONSTANT MEAN CURVATURE HYPERSURFACES IN WARPED PRODUCT SPACES
• Manifolds of Negative Curvature