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On the growth of the Bergman kernel near an infinite-type point

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Abstract

We study diagonal estimates for the Bergman kernels of certain model domains in \({\mathbb{C}^{2}}\) 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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  1. Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India

    Gautam Bharali

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  1. Gautam Bharali
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Correspondence to Gautam Bharali.

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This work is supported in part by a grant from the UGC under DSA-SAP, Phase IV.

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Bharali, G. On the growth of the Bergman kernel near an infinite-type point. Math. Ann. 347, 1–13 (2010). https://doi.org/10.1007/s00208-009-0421-x

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  • DOI: https://doi.org/10.1007/s00208-009-0421-x

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