vix.ing · top · new · best · stats · spec

A new characterization of L2-domains of holomorphy with null thin complements via L2-optimal conditions

2024/01/10 by Zhuo Liu, Xujun Zhang, Liu, Zhuo +1
Mathematics · #32D05 #32W05 #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2401.05082

openalex publication_date 2024/01/10 · openalex created_date 2024/01/13 · openalex updated_date 2026/07/28

Abstract

In this paper, we show that the L2-optimal condition implies the L2-divisibility of L2-integrable holomorphic functions. As an application, we offer a new characterization of bounded L2-domains of holomorphy with null thin complements using the L2-optimal condition, which appears to be advantageous in addressing a problem proposed by Deng-Ning-Wang. Through this characterization, we show that a domain in a Stein manifold with a null thin complement, admitting an exhaustion of complete Kähler domains, remains Stein. By the way, we construct an L2-optimal domain that does not admit any complete Kähler metric.

Related