https://neckpinch.com/authors/vincent-guedj/New arXiv papers by Vincent Guedj, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT 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 https://arxiv.org/abs/2511.13473arxiv: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