https://neckpinch.com/authors/valentino-tosatti/New arXiv papers by Valentino Tosatti, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2602.19913arxiv:2602.19913Mon, 23 Feb 2026 00:00:00 GMTMan-Chun Lee, Valentino Tosatti, Junsheng Zhang — We show that the normalized Kähler-Ricci flow on a compact Kähler manifold with semiample canonical bundle converges in the Gromov-Hausdorff topology to the metric completion of the twisted Kähler-Einstein metric on the canonical model, as conjectured by Song-Tian's analytic mimimal model program.Ricci flowKähler–Ricci flowEinstein metricsKähler geometryLimit spaces & RCDLong-time existence & convergenceKähler–Einstein & K-stabilityAnalytic minimal model program https://arxiv.org/abs/2405.04444arxiv:2405.04444Tue, 07 May 2024 00:00:00 GMTValentino Tosatti — We survey some recent developments on solutions of the Kähler-Ricci flow on compact Kähler manifolds which exist for all positive times.Ricci flowKähler–Ricci flowKähler geometryLong-time existence & convergence https://arxiv.org/abs/2405.04208arxiv:2405.04208Tue, 07 May 2024 00:00:00 GMTHans-Joachim Hein, Man-Chun Lee, Valentino Tosatti — We consider the Kähler-Ricci flow on compact Kähler manifolds with semiample canonical bundle and intermediate Kodaira dimension, and show that the flow collapses to a canonical metric on the base of the Iitaka fibration in the locally smooth topology and with bounded Ricci curvature away from the singular fibers. This follows from an asymptotic expansion for the evolving metrics, in the spirit of recent work of the first and third-named authors on collapsing Calabi-Yau metrics, and proves two conjectures of Song and Tian.Ricci flowKähler–Ricci flowRicci-flat & Calabi–Yau(Non)collapsingKähler geometryLong-time existence & convergenceAnalytic minimal model program https://arxiv.org/abs/2107.12928arxiv:2107.12928Tue, 27 Jul 2021 00:00:00 GMTValentino Tosatti, Ben Weinkove — We give a survey on the Chern-Ricci flow, a parabolic flow of Hermitian metrics on complex manifolds. We emphasize open problems and new directions.Ricci flowGeneralized & G₂ flows