On multiplicity bounds for Schrodinger eigenvalues on Riemannian surfaces

Abstract

A classical result by Cheng in 1976, improved later by Besson and Nadirashvili, says that the multiplicities of the eigenvalues of the Schrodinger operator with a smooth potential on a compact Riemannian surface M are bounded in terms of the eigenvalue index and the genus of M. We prove that these multiplicity bounds hold for an L^p-potential, where p>1. We also discuss similar multiplicity bounds for Laplace eigenvalues on singular Riemannian surfaces.

22 pages, revised version, minor stylistic corrections made, misprints corrected, to appear in Analysis & PDE

References in corpus (1)

• Les surfaces à courbure intégrale bornée au sens d'Alexandrov

Cited by in corpus (3)

• Non-degeneracy and uniqueness of solutions to singular mean field equations on bounded domains
• Conformal optimization of eigenvalues on surfaces with symmetries
• Eigenvalue inequalities on Riemannian manifolds with a lower Ricci curvature bound