Spectrum of the complex laplacian on product domains

Debraj Chakrabarti

doi:10.1090/s0002-9939-10-10522-x

Spectrum of the complex laplacian on product domains

Debraj Chakrabarti

Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

We show that the spectrum of the complex Laplacian □ 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 ∂̄ is closed on a product manifold, provided it is closed on each factor manifold.

Original language	English
Pages (from-to)	3187-3202
Number of pages	16
Journal	Proceedings of the American Mathematical Society
Volume	138
Issue number	9
DOIs	https://doi.org/10.1090/s0002-9939-10-10522-x
State	Published - Sep 2010

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AB - We show that the spectrum of the complex Laplacian □ 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 ∂̄ is closed on a product manifold, provided it is closed on each factor manifold.

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Spectrum of the complex laplacian on product domains

Abstract

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