References & Citations
Mathematics > Complex Variables
Title: A new characterization of $L^2$-domains of holomorphy with null thin complements via $L^2$-optimal conditions
(Submitted on 10 Jan 2024 (v1), last revised 17 May 2024 (this version, v3))
Abstract: In this paper, we show that the $L^2$-optimal condition implies the $L^2$-divisibility of $L^2$-integrable holomorphic functions. As an application, we offer a new characterization of bounded $L^2$-domains of holomorphy with null thin complements using the $L^2$-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 K\"ahler domains, remains Stein. By the way, we construct an $L^2$-optimal domain that does not admit any complete K\"ahler metric.
Submission history
From: Xujun Zhang [view email][v1] Wed, 10 Jan 2024 11:36:51 GMT (13kb)
[v2] Thu, 8 Feb 2024 11:11:43 GMT (12kb)
[v3] Fri, 17 May 2024 14:28:38 GMT (16kb)
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