Spectral properties of Schrödinger operators on compact manifolds: rigidity, flows, interpolation and spectral estimates

DOI10.1016/j.crma.2013.06.014zbMath1276.58007arXiv1303.2790OpenAlexW2964182664MaRDI QIDQ367182

Michael Loss, Maria J. Esteban, Jean Dolbeault, A. A. Laptev

Publication date: 26 September 2013

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.2790

zbMATH Keywords

Schrödinger operatorscompact connected Riemannian manifolds without boundaryoptimal spectral estimates

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Elliptic equations on manifolds, general theory (58J05) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (10)

Magnetic rings ⋮ On the proportionality of Chern and Riemannian scalar curvatures ⋮ Improved interpolation inequalities and stability ⋮ Uniqueness and rigidity in nonlinear elliptic equations, interpolation inequalities, and spectral estimates ⋮ Keller-Lieb-Thirring inequalities for Schrödinger operators on cylinders ⋮ The lowest eigenvalue of Schrödinger operators on compact manifolds ⋮ Interpolation inequalities and spectral estimates for magnetic operators ⋮ Rigidity versus symmetry breaking via nonlinear flows on cylinders and Euclidean spaces ⋮ The Moser-Trudinger-Onofri inequality ⋮ On a class of sharp multiplicative Hardy inequalities

Cites Work

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• Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations
• Sobolev inequalities and Myers's diameter theorem for an abstract Markov generator
• Sharp interpolation inequalities on the sphere: new methods and consequences
• Nonlinear flows and rigidity results on compact manifolds
• Spectral estimates on the sphere
• Global and local behavior of positive solutions of nonlinear elliptic equations

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