The Poletsky-Rosay theorem on singular complex spaces

TL;DR

This paper extends a key theorem in complex analysis, the Poletsky-Rosay theorem, to apply to singular complex spaces, broadening its applicability in the study of plurisubharmonic functions.

Contribution

The paper generalizes the Poletsky-Rosay theorem to locally irreducible complex spaces, addressing the case of singularities.

Findings

Poletsky-Rosay theorem extended to singular spaces

Plurisubharmonicity of Poisson envelopes established in new setting

Broader applicability in complex analysis and geometry

Abstract

In this paper we extend the Poletsky-Rosay theorem, concerning plurisubharmonicity of the Poisson envelope of an upper semicontinuous function, to locally irreducible complex spaces.