Upper bounds for the first eigenvalue of the operator \(L_r\) and some applications
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Publication:5954290
zbMath0990.53058MaRDI QIDQ5954290
Fernando Codá Marques, Manfredo Perdigão do Carmo, Hilário Alencar
Publication date: 17 February 2002
Published in: Illinois Journal of Mathematics (Search for Journal in Brave)
principal curvatures\(r\)-mean curvaturesfirst eigenvaluesNewton transformationoperator \(L_r\) of the \(r\)-mean curvaturestability operator
Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40)
Related Items (8)
Optimal upper estimates for the first eigenvalue of a Jacobi type operator in spherical and hyperbolical spaces ⋮ Reilly type inequality for the first eigenvalue of the \(L_{r;F}\) operator ⋮ Estimates for eigenvalues of ℒr operator on self-shrinkers ⋮ Sharp upper bounds for \(\lambda _1^{L_r}\) of immersed hypersurfaces and their stability in space forms ⋮ Extrinsic upper bound of the eigenvalue for \(p\)-Laplacian ⋮ Estimates for eigenvalues of the operator \(L_r\) ⋮ Pinching of the first eigenvalue for second order operators on hypersurfaces of the Euclidean space ⋮ Inequalities for eigenvalues of elliptic operators in divergence form on Riemannian manifolds
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