https://neckpinch.com/authors/chinh-h-lu/New arXiv papers by Chinh H. Lu, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.06473arxiv: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://arxiv.org/abs/2607.08325arxiv:2607.08325Thu, 09 Jul 2026 00:00:00 GMTEleonora Di Nezza, Vincent Guedj, Chinh Hoang Lu — We study the geometric regularization of a positive closed current by the (twisted) Kähler-Ricci flow on a compact Kähler manifold. We conjecture that the local Arnold multiplicities linearly decrease to zero, while the flow produces complete Kähler metrics in the Zariski open subset of points that have small Lelong numbers. We prove this conjecture in complex dimension 1 and provide several partial results in higher dimension.Ricci flowKähler–Ricci flowKähler geometry https://arxiv.org/abs/2606.15816arxiv:2606.15816Sun, 14 Jun 2026 00:00:00 GMTEleonora Di Nezza, Vincent Guedj, Chinh H. Lu — We study the geometric regularization of positive closed currents by the Kähler-Ricci flow on compact Kähler manifolds. In a previous work of ours, it was shown that the Kähler-Ricci flow immediately smoothes out such a current when it has zero Lelong numbers. We study here the case when T₀ has divisorial singularities, showing that the flow gradually replaces the latter by Poincaré type ones, providing an approximation of T₀ by complete Kähler metrics with bounded curvature in a Zariski open set.Ricci flowKähler–Ricci flowSingularitiesKähler geometry