https://neckpinch.com/authors/papa-badiane/New arXiv papers by Papa Badiane, 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