Geometry and Topology of the space of plurisubharmonic functions

Soufian Abja

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arXiv · 1703.05556

Geometry and Topology of the space of plurisubharmonic functions

Soufian Abja

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Abstract

Let $\Omega$ be a strongly pseudoconvex domain. We introduce the Mabuchi space of strongly plurisubharmonic functions in $\Omega$. We study metric properties of this space using Mabuchi geodesics and establish regularity properties of the latter, especially in the ball. As an application we study the existence of local K\"ahler-Einstein metrics.

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Soufian Abja. 2017-03-16. Geometry and Topology of the space of plurisubharmonic functions. https://arxiv.org/abs/1703.05556

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