Equidistribution theorems on strongly pseudoconvex domains

2017/08/03 by Chin-Yu Hsiao, Hsiao, Chin-Yu, Guokuan Shao +1
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1708.01094

openalex publication_date 2017/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 S¹ 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 M.

Related

• Torus equivariant Szegő kernel asymptotics on strongly pseudoconvex CR manifolds
• On the coefficients of the equivariant Szegő kernel asymptotic expansions
• Szegő kernels and equivariant embedding theorems for CR manifolds
• Semi-classical asymptotics of partial Bergman kernels on ℝ-symmetric complex manifolds with boundary
• Superlogarithmic estimates on pseudoconvex domains and CR manifolds