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arXiv · 2410.12715

Sobolev Regularity for the Bergman Projection on Relatively Compact Domains in Hermitian manifolds

Phillip S. Harrington
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Abstract

Generalizing a result of Berndtsson and Charpentier, we provide sufficient conditions for $L^2$ Sobolev regularity of the Bergman projection acting on $L^2$ sections of a holomorphic line bundle restricted to a relatively compact domain with Lipschitz boundary in a Hermitian manifold. We provide examples to show that our methods work for domains in Hopf manifolds endowed with a suitable Hermitian metric.

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Phillip S. Harrington. 2024-10-16. Sobolev Regularity for the Bergman Projection on Relatively Compact Domains in Hermitian manifolds. https://arxiv.org/abs/2410.12715

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