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Spectrum of the complex Laplacian on product domains


Author: Debraj Chakrabarti
Journal: Proc. Amer. Math. Soc. 138 (2010), 3187-3202
MSC (2010): Primary 32W05; Secondary 35P10, 35N15
DOI: https://doi.org/10.1090/S0002-9939-10-10522-X
Published electronically: May 12, 2010
MathSciNet review: 2653944
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Abstract: We show that the spectrum of the complex Laplacian $ \Box$ on a product of Hermitian manifolds is the Minkowski sum of the spectra of the complex Laplacians on the factors. We use this to show that the range of the Cauchy-Riemann operator $ \overline{\partial}$ is closed on a product manifold, provided it is closed on each factor manifold.


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Additional Information

Debraj Chakrabarti
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: dchakrab@nd.edu

DOI: https://doi.org/10.1090/S0002-9939-10-10522-X
Received by editor(s): November 17, 2009
Published electronically: May 12, 2010
Communicated by: Franc Forstneric
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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