Universal inequalities for the eigenvalues of Schrodinger operators on submanifolds

Autor: Soufi, Ahmad El, Harrell, Evans, Ilias, Said
Rok vydání: 2009
Předmět:
Zdroj: Transactions of the American Mathematical Society 361, 5 (2009) 2337--2350
Druh dokumentu: Working Paper
Popis: We establish inequalities for the eigenvalues of Schr\"odinger operators on compact submanifolds (possibly with nonempty boundary) of Euclidean spaces, of spheres, and of real, complex and quaternionic projective spaces, which are related to inequalities for the Laplacian on Euclidean domains due to Payne, P\'olya, and Weinberger and to Yang, but which depend in an explicit way on the mean curvature. In later sections, we prove similar results for Schr\"odinger operators on homogeneous Riemannian spaces and, more generally, on any Riemannian manifold that admits an eigenmap into a sphere, as well as for the Kohn Laplacian on subdomains of the Heisenberg group. Among the consequences of this analysis are an extension of Reilly's inequality, bounding any eigenvalue of the Laplacian in terms of the mean curvature, and spectral criteria for the immersibility of manifolds in homogeneous spaces.
Comment: A paraitre dans Transactions of the AMS
Databáze: arXiv