Spectrum of the complex Laplacian on product domains

Details Spectrum of the complex Laplacian on product domains Spectrum of the complex Laplacian on product domains

2009-11-18

arxiv.org/abs/0911.3451v2

Mathematics

Complex Variables

Minor typos fixed; to appear in the Proceedings of the AMS.

Scientific paper

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 fact to show that the range of the d-bar operator on a
product manifold is closed, provided it is closed in each factor.

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