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arXiv · 1708.01094

Equidistribution theorems on strongly pseudoconvex domains

Chin-Yu Hsiao·Guokuan Shao
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Abstract

This work consists of two parts. In the first part, we consider a compact connected strongly pseudoconvex CR manifold $X$ with a transversal CR $S^{1}$ action. We establish an equidistribution theorem on zeros of CR functions. The main techniques involve a uniform estimate of Szeg\H{o} kernel on $X$. In the second part, we consider a general complex manifold $M$ with a strongly pseudoconvex boundary $X$. By using classical result of Boutet de Monvel-Sj\"ostrand about Bergman kernel asymptotics, we establish an equidistribution theorem on zeros of holomorphic functions on $\overline M$.

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Chin-Yu Hsiao, Guokuan Shao. 2017-08-03. Equidistribution theorems on strongly pseudoconvex domains. https://arxiv.org/abs/1708.01094

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