https://neckpinch.com/authors/giovanni-gentili/New arXiv papers by Giovanni Gentili, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2610.07897/arxiv: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://neckpinch.com/papers/2303.02689/arxiv: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