Heat kernel estimates for the $\bar\partial$-Neumann problem on $G$-manifolds

TL;DR

This paper establishes heat kernel estimates for the $ar ext{d}$-Neumann Laplacian on noncompact, strongly pseudoconvex complex manifolds with Lie group symmetry, linking these results to Laplace-Beltrami operators.

Contribution

It provides new heat kernel estimates for the $ar ext{d}$-Neumann problem on complex manifolds with symmetry, extending understanding to noncompact settings.

Findings

Heat kernel estimates for the $ar ext{d}$-Neumann Laplacian are derived.

Results connect the $ar ext{d}$-Neumann Laplacian to Laplace-Beltrami operators.

The study applies to manifolds with Lie group symmetry and compact quotients.

Abstract

We prove heat kernel estimates for the $\bar\partial$-Neumann Laplacian acting in spaces of differential forms over noncompact, strongly pseudoconvex complex manifolds with a Lie group symmetry and compact quotient. We also relate our results to those for an associated Laplace-Beltrami operator on functions.