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

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Abstract

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

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  1. Fakultät für Mathematik, Universität Wien, Vienna, Austria

    Joe J. Perez

  2. Fakultät für Mathematik, Technische Universität, Chemnitz, Germany

    Peter Stollmann

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  1. Joe J. Perez
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Correspondence to Peter Stollmann.

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Dedicated to Barry Simon in celebration of his 65th birthday.

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Perez, J.J., Stollmann, P. Heat kernel estimates for the \({{\bar{\partial}}}\) -Neumann problem on G-manifolds. manuscripta math. 138, 371–394 (2012). https://doi.org/10.1007/s00229-011-0496-z

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