Spectrum of the complex laplacian on product domains

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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 languageEnglish
Pages (from-to)3187-3202
Number of pages16
JournalProceedings of the American Mathematical Society
Issue number9
StatePublished - Sep 2010


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