A new characterization of the CR shpere and the sharp eigenvalue estimate for the Kohn Laplacian

Abstract

Motivated by a sharp eigenvalue estimate for the Kohn Laplacian, we prove a theorem that characterizes the CR sphere in terms of the existence of a non-trivial complex-valued function satisfying a certain overdetermined system.

added a section on the spectral theory of the Kohn Laplacian. revised