A New Characterization of $$L^2$$ -Domains of Holomorphy with Null Thin Complements via $$L^2$$ -Optimal Conditions

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 Kähler domains, remains Stein. By the way, we construct an \(L^2\)-optimal domain that does not admit any complete Kähler metric.