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

By Jean Dolbeault A, Maria J. Esteban A, Ari Laptev B and Michael Loss C


This note is devoted to optimal spectral estimates for Schrödinger operators on compact connected Riemannian manifolds without boundary. These estimates are based on the use of appropriate interpolation inequalities and on some recent rigidity results for nonlinear elliptic equations on those manifolds

Topics: interpolation, Gagliardo-Nirenberg inequalities, rigidity results, Lieb-Thirring inequalities, fast diffusion equation, Laplace-Beltrami operator, Schrödinger equation, eigenvalues, spectral estimates, optimal constants, compact manifolds, Ricci curvature, Ricci tensor
Year: 2013
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