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

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.

22 pages

References in corpus (5)

• Essential self-adjointness, generalized eigenforms, and spectra for the $\bar{\partial }$-Neumann problem on $G$-manifolds
• A transversal Fredholm property for the $\bar{\partial }$-Neumann problem on $G$-bundles
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• Unitary representations of unimodular Lie groups in Bergman spaces
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Cited by in corpus (1)

• Essential self-adjointness, generalized eigenforms, and spectra for the $\bar{\partial }$-Neumann problem on $G$-manifolds