Title: Isoperimetric inequalities for the eigenvalues of natural Schroedinger operators on surfaces

Authors: Ahmad El Soufi

Issue: Volume 58 (2009), Issue 1, 335-350

Abstract: This paper deals with eigenvalue optimization problems for a family of natural Schr\"odinger operators arising in some geometrical or physical contexts. These operators, whose potentials are quadratic in curvature, are considered on closed surfaces immersed in space forms and we look for geometries that maximize the eigenvalues. We show that under suitable assumptions on the potential, the first and the second eigenvalues are maximized by (round) spheres.