Equidistribution theorems on strongly pseudoconvex domains

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 $\overline{M}$.

26 pages

References in corpus (1)

• Distribution of zeros of random and quantum chaotic sections of positive line bundles