On the Laplace operator penalized by mean curvature

DOI10.1007/s002200050406zbMath0928.35028OpenAlexW2005457844MaRDI QIDQ1291002

Michael Loss, Evans M. II. Harrell

Publication date: 6 October 1999

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s002200050406

zbMATH Keywords

hypersurfaceLaplace-Beltrami operatorprincipal curvaturessecond eigenvalue

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

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On the Cauchy Problem for a Dynamical Euler's Elastica ⋮ Isoperimetric inequalities for eigenvalues of the Laplacian and the Schrödinger operator ⋮ On the 𝐿ᵣ-operators penalized by (𝑟+1)-mean curvature ⋮ An isoperimetric type inequality for the principal eigenvalue of Schrödinger operators depending on the curvature of a loop ⋮ A geometric characterization of a sharp Hardy inequality ⋮ Critical potentials of the eigenvalue ratios of Schrödinger operators ⋮ Characterization of hypersurfaces via the second eigenvalue of the Jacobi operator ⋮ A lower bound for the ground state energy of a Schrödinger operator on a loop ⋮ Commutators, Eigenvalue Gaps, and Mean Curvature in the Theory of Schrödinger Operators ⋮ On an isoperimetric inequality for a Schrödinger operator depending on the curvature of a loop

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