https://neckpinch.com/authors/ahmed-zeriahi/New arXiv papers by Ahmed Zeriahi, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2610.06473/arxiv:2610.06473Mon, 05 Oct 2026 00:00:00 GMTPapa Badiane, Chinh H. Lu, Ahmed Zeriahi — We study regularity of bounded weak solutions to complex Monge-Ampère equations on compact Hermitian manifolds with right-hand side possibly decreasing in the unknown. Our proof relies on the domination principle and a priori estimates, partially motivated by the Monge-Ampère eigenvalue problem. Our main result roughly says that any bounded solution is smooth in the regular locus of the data. When the right-hand side is strictly positive and smooth, we recover known results by Nie, Ko lodziej-Nguyen for the Hermitian case and Székelyhidi-Tosatti for the Kähler case, which rely on the regularizing property of the Kähler-Ricci flow.Ricci flowWeak & singular flowsEigenvalues & spectrum https://neckpinch.com/papers/2511.13473/arxiv:2511.13473Mon, 17 Nov 2025 00:00:00 GMTAlix Deruelle, Vincent Guedj, Henri Guenancia, Ahmed Zeriahi — Given a compact Kähler manifold X and a closed, positive (1,1)-current T on X, we find sufficient conditions for T to induce a metric structure (X,d_T) which is the Gromov-Hausdorff limit of compact Kähler manifolds either in a "static" way or at time zero of smooth Kähler-Ricci flows. In dimension 1 we extend works of T. Richard and M. Simon, showing that any oriented compact Alexandrov surface with bounded integral curvature and without cusp is the initial datum of a Kähler-Ricci flow.Ricci flowKähler–Ricci flowKähler geometryWeak & singular flowsLimit spaces & RCD