Soufian Abja

activity

20172024

collaborators

6 papers

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.AP2021

Viscosity solutions to complex first eigenvalue equations

Soufian Abja

We study the viscosity solutions to the first eigenvalue equation. We consider $Ω$ a bounded B-regular domain in $C^{n}$ and we prove that the Dirichlet problem $Λ_{1}(D_{\m…

math.AP2021

Local regularity for concave homogeneous complex degenerate elliptic equations comparable to the Monge-Ampère equation

Soufian Abja, Guillaume Olive

In this paper, we establish a local regularity result for $W_{loc}^{2, p}$ solutions to complex degenerate nonlinear elliptic equations $F (D_{C}^{2} u) = f$ when they…

math.AP2020

Uniform estimates for concave homogeneous complex degenerate elliptic equations comparable to the Monge-Ampère equation

Soufian Abja, Sławomir Dinew, Guillaume Olive

We prove sharp uniform estimates for strong supersolutions of a large class of fully nonlinear degenerate elliptic complex equations. Our findings rely on ideas of Kuo and Trudinge…

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 $Ω$ be a strongly pseudoconvex domain. We introduce the Mabuchi space of strongly plurisubharmonic functions in $Ω$ . We study metric properties of this space using Mabuchi geod…