https://neckpinch.com/authors/luigi-vezzoni/New arXiv papers by Luigi Vezzoni, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.07897arxiv:2610.07897Tue, 06 Oct 2026 00:00:00 GMTGiovanni Gentili, Luigi Vezzoni — We study the HKT geometry of compact locally conformally hyperkähler manifolds. We prove that on these manifolds the quaternionic Monge-Ampère equation is always solvable, extending results of Alesker and of Dinew-Sroka, and we confirm the conjecture on the maximal existence time of the HKT-Ricci flow. On quaternionic Hopf surfaces we construct non-trivial HKT solitons and prove convergence of the normalized flow for symmetric initial data.Ricci flowRicci-flat & Calabi–YauKähler geometryHomogeneous spaces https://arxiv.org/abs/2604.18195arxiv:2604.18195Mon, 20 Apr 2026 00:00:00 GMTMarco Gallo, Luigi Vezzoni — We establish a general result ensuring a C¹ a priori bound for smooth curves of Hermitian metrics. As a main application, we obtain a new regularity result for Hermitian curvature flows, and in particular for the second Chern-Ricci flow.Ricci flowGeneralized & G₂ flowsKähler geometry https://arxiv.org/abs/2407.17061arxiv:2407.17061Wed, 24 Jul 2024 00:00:00 GMTLucio Bedulli, Luigi Vezzoni — We study the flow of Hermitian metrics governed by the second Chern-Ricci form on a compact complex manifolds. The flow belongs to the family of Hermitian curvature flows introduced by Streets and Tian and it was considered by Lee in order to study compact Hermitian manifolds with almost negative Chern bisectional curvature. We show a regularity result on compact complex parallelizable manifolds and we prove that Chern-flat metrics are dynamically stable.Ricci flowGeneralized & G₂ flows https://arxiv.org/abs/2303.02689arxiv:2303.02689Sun, 05 Mar 2023 00:00:00 GMTLucio Bedulli, Giovanni Gentili, Luigi Vezzoni — We show that the parabolic quaternionic Monge-Ampère equation on a compact hyperkähler manifold has always a long-time solution which once normalized converges smoothly to a solution of the quaternionic Monge-Ampère equation. This is the same setting in which Dinew and Sroka prove the conjecture of Alesker and Verbitsky. We also introduce an analogue of the Chern-Ricci flow in hyperhermitian manifolds.Ricci flowGeneralized & G₂ flowsRicci-flat & Calabi–YauKähler geometryLong-time existence & convergence