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

2018/10/24 by Pawlaschyk, Thomas, Zeron, Eduardo S. · 1 citation
#31C10 #Complex Variables (math.CV) #FOS: Mathematics #Primary 32U05 #Secondary 35D40

paper · doi:10.48550/arxiv.1810.10512

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 ℂⁿ.

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• On rigid q-plurisubharmonic functions and q-pseudoconvex tube domains in ℂⁿ

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