Abstract
We introduce a condition, called Property -K, which encodes information about the holomorphic structure of fat subdomains. We obtain an equivalence between this condition and the compactness of the $\overline{\partial}$-Neumann operator in any convex domain. We also exhibit a local property of the Kobayashi metric under which the domain is locally a product space.
Citation
Mijoung Kim. "The $\overline{\partial}$-Neumann operator and the Kobayashi metric." Illinois J. Math. 48 (2) 635 - 643, Summer 2004. https://doi.org/10.1215/ijm/1258138403
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