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math.CV2024
Regularity of geodesics in the spaces of convex and plurisubharmonic functions II
Soufian Abja, Slawomir Dinew
In this note we continue our investigation of geodesics in the space of convex and plurisubharmonic functions. We show optimal regularity for geodesics joining two smooth strictly…
math.CV2019
Regularity of geodesics in the spaces of convex and plurisubharmonic functions
Soufian Abja, Slawomir Dinew
In this note we investigate the regularity of geodesics in the space of convex and plurisubharmonic functions. In the real setting we prove (optimal) local C^{1,1} regularity. We c…
math.CV2017
Geometry and Topology of the space of plurisubharmonic functions
Soufian Abja
Let be a strongly pseudoconvex domain. We introduce the Mabuchi space of strongly plurisubharmonic functions in . We study metric properties of this space using Mabuchi geod…