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arXiv · 1810.10512

On convex hulls and pseudoconvex domains generated by $q$-plurisubharmonic functions, part III

Thomas Pawlaschyk·Eduardo S. Zeron
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Abstract

We characterise in this work the $q$-plurisubharmonic functions in terms of the theory of viscosity solutions. We show that an upper semicontinuous function is $q$-plurisubharmonic if and only if its complex Hessian has at most $q$ strictly negative eigenvalues in the viscosity sense. This characterisation is then used to prove that the supremum convolution of a (strictly) $q$-plurisubharmonic function is again (strictly) $q$-plurisubharmonic on a maybe different set of definition. Finally, we use the supremum convolution to deduce a new characterisation for the $q$-pseudoconvex subsets in $\mathbb{C}^n$.

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Thomas Pawlaschyk, Eduardo S. Zeron. 2018-10-24. On convex hulls and pseudoconvex domains generated by $q$-plurisubharmonic functions, part III. https://arxiv.org/abs/1810.10512

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