Upper bound for the second eigenvalue of a Schrödinger operator on a compact manifold and applications

DOI10.1016/0022-1236(92)90123-ZzbMath0766.58055OpenAlexW1977214601MaRDI QIDQ1188096

Said Ilias, Ahmad El Soufi

Publication date: 13 August 1992

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(92)90123-z

zbMATH Keywords

Schrödinger operatorRiemannian manifoldspectrumminimal hypersurfacesisospectrality

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50)

Related Items

Stability for hypersurfaces of constant mean curvature with free boundary, Unnamed Item, A spectral characterization of the $H(r)$-torus by the first stability eigenvalue, Sharp Reilly-type inequalities for a class of elliptic operators on submanifolds, Rigidity of Hawking mass for surfaces in three manifolds, The spectrum of the Laplacian: A geometric approach, Stable complete surfaces with constant mean curvature, The spaces of index one minimal surfaces and stable constant mean curvature surfaces embedded in flat three manifolds, A lower bound on the spectrum of the Sublaplacian, The second variation of nonorientable minimal submanifolds, Spectre et géométrie conforme des variétés compactes à bord, On the concentration-compactness phenomenon for the first Schrödinger eigenvalue, Minimal immersions of compact bordered Riemann surfaces with free boundary, A Reilly inequality for some natural elliptic operators on hypersurfaces, Critical potentials of the eigenvalues and eigenvalue gaps of Schrödinger operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Homogeneous minimal hypersurfaces in the unit spheres and the first eigenvalues of their Laplacian
• Stability of hypersurfaces with constant mean curvature
• Minimal immersions of surfaces by the first eigenfunctions and conformal area
• Stability of hypersurfaces of constant mean curvature in Riemannian manifolds
• Isospectral sets of conformally equivalent metrics
• Immersions minimales, première valeur propre du laplacien et volume conforme. (Minimal immersions, first eigenvalue of the Laplacian and conformal volume)
• Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature
• Some spectral results for the Laplace operator with potential on the n- sphere
• Some spectral results on rank one symmetric spaces
• Some inverse spectral results for negatively curved 2-manifolds
• The first eigenvalue of the Laplacian on tori
• Spectral theory on S**2: some open questions
• A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces
• An inequality of ``Reilly-type for submanifolds of the hyperbolic space
• The spectral geometry of a Riemannian manifold
• On manifolds of negative curvature with isospectral potentials
• Minimal varieties in Riemannian manifolds
• Another Report on Harmonic Maps