5 papers · 1 filter
HKT geometry on locally conformally hyperkähler manifolds
Giovanni 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, extendin…
Continuous solutions to the quaternionic Monge-Ampère equation on locally flat HKT manifolds
Giovanni Gentili, Antonio Trusiani, Luigi Vezzoni
We prove that on a compact locally flat HKT manifold the quaternionic Monge--Ampère equation always has a unique continuous solution. This provides new evidence for the Conjecture…
Long-time existence of the pluriclosed flow on some fibrations
Elia Fusi, James Stanfield, Luigi Vezzoni
We prove long-time existence of the pluriclosed flow on certain compact quotients of Lie groups for non-invariant initial data, as well as on some holomorphic principal torus bundl…
A note on the pluriclosed flow on balanced manifolds with
Anna Fino, Luigi Vezzoni
We conjecture that on any compact balanced manifold with , the pluriclosed flow admits long-time solutions for every initial pluriclosed metric, and…
On the Calabi estimate of geometric flows of Hermitian metrics
Marco Gallo, Luigi Vezzoni
We establish a general result ensuring a a priori bound for smooth curves of Hermitian metrics. As a main application, we obtain a new regularity result for Hermitian curvatu…