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

References in corpus (1)

• Embeddability for Three-Dimensional Cauchy-Riemann Manifolds and CR Yamabe Invariants

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• Sharp Hardy-Littlewood-Sobolev inequalities on compact CR manifold
• The Lichnerowicz--Obata theorem for the Kohn Laplacian in three dimensions
• The Webster scalar curvature and sharp upper and lower bounds for the first positive eigenvalue of the Kohn-Laplacian on real hypersurfaces
• An upper bound for the first positive eigenvalue of the Kohn Laplacian on Reinhardt real hypersurfaces
• Eigenvalues of the Kohn Laplacian and deformations of pseudohermitian structures on CR manifolds
• Semi-isometric CR immersions of CR manifolds into Kähler manifolds and applications
• On the Obata theorem for the weighted Kohn Laplacian in a closed weighted Sasakian manifold
• The Obata first eigenvalue theorems on a seven dimensional quaternionic contact manifold
• The holomorphic sectional curvature and "convex" real hypersurfaces in Kähler manifolds