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Bounded Plurisubharmonic Exhaustion Functions for Lipschitz Pseudoconvex Domains in $\mathbb{CP}^n$ (1510.03737v1)
Published 13 Oct 2015 in math.CV
Abstract: In this paper, we use Takeuchi's Theorem to show that for every Lipschitz pseudoconvex domain $\Omega$ in $\mathbb{CP}n$ there exists a Lipschitz defining function $\rho$ and an exponent $0<\eta<1$ such that $-(-\rho)\eta$ is strictly plurisubharmonic on $\Omega$. This generalizes a result of Ohsawa and Sibony for $C2$ domains. In contrast to the Ohsawa-Sibony result, we provide a counterexample demonstrating that we may not assume $\rho=-\delta$, where $\delta$ is the geodesic distance function for the boundary of $\Omega$.