On the growth of the Bergman kernel near an infinite-type point |
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Authors: | Gautam Bharali |
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Institution: | (1) Department of Mathematics, Ohio State University, Columbus, OH 43210, USA |
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Abstract: | We study diagonal estimates for the Bergman kernels of certain model domains in
\mathbbC2{\mathbb{C}^{2}} near boundary points that are of infinite type. To do so, we need a mild structural condition on the defining functions of
interest that facilitates optimal upper and lower bounds. This is a mild condition; unlike earlier studies of this sort, we are able to make estimates for
non-convex pseudoconvex domains as well. This condition quantifies, in some sense, how flat a domain is at an infinite-type boundary
point. In this scheme of quantification, the model domains considered below range—roughly speaking—from being “mildly infinite-type”
to very flat at the infinite-type points. |
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Keywords: | |
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