School of Mathematics and Natural Sciences

Seminar: Tobias Harz

02.06.2022|16:15 Uhr

On plurisubharmonic defining functions for pseudoconvex domains in C^2

(joint work with A.-K. Gallagher)

We investigate the question of existence of plurisubharmonic defining
functions for smoothly bounded, pseudoconvex domains in 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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