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The Journal of Geometric Analysis

, Volume 29, Issue 1, pp 510–541 | Cite as

Geometry and Topology of the Space of Plurisubharmonic Functions

  • Soufian AbjaEmail author
Article
  • 57 Downloads

Abstract

Let \(\Omega \) be a strongly pseudoconvex domain. We introduce the Mabuchi space of strongly plurisubharmonic functions in \(\Omega \). We study the 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 Kähler–Einstein metrics.

Keywords

Geodesics Mabuchi space Monge–Ampère equation Pseudoconvex domain 

Mathematics Subject Classification

53C55 32W20 32U05 

Notes

Acknowledgements

The author is grateful for his supervisors Vincent Guedj and Said Asserda, for their support, suggestions and encouragement. The author wants to thank Ahmed Zeriahi for his very useful discussions and suggestions. The author would also like to thank Tat Dat Tô and Zakarias Sjöström Dyrefelt for their very careful reading of the preliminary version of this paper and their very useful discussions. This work has been finalized while the author was visiting the “Institut de Mathématiques de Toulouse” in march 2017 and he would like to thank them for their hospitality.

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Copyright information

© Mathematica Josephina, Inc. 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of SciencesIbn Tofail UniversityKenitraMorocco

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