Equidistribution theorems on strongly pseudoconvex domains

Hsiao, Chin-Yu; Shao, Guokuan

doi:10.1090/tran/7688

Equidistribution theorems on strongly pseudoconvex domains
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by Chin-Yu Hsiao and Guokuan Shao PDF

Trans. Amer. Math. Soc. 372 (2019), 1113-1137 Request permission

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 Szegő 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–Sjöstrand about Bergman kernel asymptotics, we establish an equidistribution theorem on zeros of holomorphic functions on $\overline {M}$.

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