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

TL;DR

This paper characterizes the CR sphere through a new theorem involving a specific overdetermined system and provides a sharp eigenvalue estimate for the Kohn Laplacian, advancing understanding in CR geometry.

Contribution

It introduces a novel characterization of the CR sphere based on solutions to an overdetermined system related to the Kohn Laplacian.

Findings

Characterization of the CR sphere via a non-trivial complex-valued function

A sharp eigenvalue estimate for the Kohn Laplacian

New insights into CR geometry and eigenvalue problems

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.