Positivity of the $\bar\partial$-Neumann Laplacian

TL;DR

This paper investigates the spectral properties of the $areta$-Neumann Laplacian and demonstrates that the domain's pseudoconvexity can be characterized by the operator's positivity.

Contribution

It establishes a spectral theoretic characterization of pseudoconvexity via the positivity of the $areta$-Neumann Laplacian, linking geometry and spectral theory.

Findings

Positivity of the $areta$-Neumann Laplacian characterizes pseudoconvexity.

Spectral properties reflect geometric features of the domain.

The study provides a new perspective on the $areta$-Neumann problem.

Abstract

We study the $\bar\partial$-Neumann Laplacian from spectral theoretic perspectives. In particular, we show how pseudoconvexity of a bounded domain is characterized by positivity of the $\bar\partial$-Neumann Laplacian.