Sharp upper bounds for \(\lambda _1^{L_r}\) of immersed hypersurfaces and their stability in space forms

DOI10.1007/s10114-007-6322-6zbMath1154.53040OpenAlexW2336008820MaRDI QIDQ943515

Rushan Wang

Publication date: 9 September 2008

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-007-6322-6

zbMATH Keywords

stabilitygeodesic hypersphereSchrödinger-type operator\(r\)-mean curvature

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40)

Related Items (1)

REILLY INEQUALITIES OF ELLIPTIC OPERATORS ON CLOSED SUBMANIFOLDS

Cites Work

• Extrinsic upper bounds for \(\lambda _ 1\)
• Stability of hypersurfaces of constant mean curvature in Riemannian manifolds
• An inequality of ``Reilly-type for submanifolds of the hyperbolic space
• On the first eigenvalue of the Laplacian for compact submanifolds of Euclidean space
• On the first eigenvalue of the linearized operator of the \(r\)-th mean curvature of a hypersurface
• Stability of hypersurfaces with constant \(r\)-mean curvature
• Integral formulas for the \(r\)-mean curvature linearized operator of a hypersurface
• Variational properties of functions of the mean curvatures for hypersurfaces in space forms
• On the first eigenvalue of the linearized operator of the higher order mean curvature for closed hypersurfaces in space forms
• Extrinsic upper bound for the first eigenvalue of elliptic operators
• A Reilly inequality for some natural elliptic operators on hypersurfaces
• Upper bounds for the first eigenvalue of the Laplacian on compact submanifolds.
• Erratum to: On the first eigenvalue of the linearized operator of the \(r\)-th mean curvature of a hypersurface
• Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
• Upper bounds for the first eigenvalue of the operator \(L_r\) and some applications

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