On plurisubharmonic defining functions for pseudoconvex domains in $\mathbb{C}^2$

Anne-Katrin Gallagher; Tobias Harz

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arXiv · 2204.13270

On plurisubharmonic defining functions for pseudoconvex domains in $\mathbb{C}^2$

Anne-Katrin Gallagher·Tobias Harz

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Abstract

We investigate the question of existence of plurisubharmonic defining functions for smoothly bounded, pseudoconvex domains in $\mathbb{C}^2$. In particular, we construct a family of simple counterexamples to the existence of plurisubharmonic smooth local defining functions. Moreover, we give general criteria equivalent to the existence of plurisubharmonic smooth defining functions on or near the boundary of the domain. These equivalent characterizations are then explored for some classes of domains.

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Anne-Katrin Gallagher, Tobias Harz. 2022-04-28. On plurisubharmonic defining functions for pseudoconvex domains in $\mathbb{C}^2$. https://arxiv.org/abs/2204.13270

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