Spectrum of the complex Laplacian on product domains
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- by Debraj Chakrabarti PDF
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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.References
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Additional Information
- Debraj Chakrabarti
- Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
- MR Author ID: 827655
- Email: dchakrab@nd.edu
- Received by editor(s): November 17, 2009
- Published electronically: May 12, 2010
- Communicated by: Franc Forstneric
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2653944