Plurisubharmonic Defining Functions in $\mathbb C^2$

Luka Mernik

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arXiv · 2007.04264

Plurisubharmonic Defining Functions in $\mathbb C^2$

Luka Mernik

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Abstract

Let $\Omega=\{r<0\}\subset\mathbb C^2$, with $r$ plurisubharmonic on $b\Omega=\{r=0\}$. Let $\rho$ be another defining function for $\Omega$. A formula for the determinant of the complex Hessian of $\rho$ in terms of $r$ is computed. This formula is used to give necessary and sufficient conditions that make $\rho$ (locally) plurisubharmonic.

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Luka Mernik. 2020-07-08. Plurisubharmonic Defining Functions in $\mathbb C^2$. https://arxiv.org/abs/2007.04264

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