12 papers
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…
A remark on the second order estimates for the quaternionic Calabi-Yau problem on hyperkähler manifolds
Giovanni Gentili, Luigi Vezzoni
We revisit the second order estimate for solutions to the quaternionic Calabi-Yau problem on hyperkähler manifolds, originally established by Dinew and Sroka. In this note, we pres…
The heterotic G-system on 2-step nilmanifolds endowed with principal torus bundles
Andrei Moroianu, Alberto Raffero, Luigi Vezzoni
We study the geometric heterotic G-system on 7-dimensional 2-step nilmanifolds endowed with principal torus bundles and with a prescribed flat tangent bundle…
The holonomy of the Obata connection on Joyce hypercomplex manifolds
Beatrice Brienza, Udhav Fowdar, Giovanni Gentili +1
We study the holonomy of the Obata connection on Joyce hypercomplex manifolds. For all such group manifolds except , we show that the holonomy group is strictly…
$\del\delbar$-Lemma and Bott-Chern cohomology of twistor spaces
Anna Fino, Gueo Grantcharov, Nicoletta Tardini +2
In the paper we study the Bott-Chern and Aeppli cohomologies of the twistor space of a compact self-dual 4-manifold and we characterize the validity of the $\partial \overline \par…
Fully non-linear elliptic equations on compact hyperkähler manifolds
Giovanni Gentili, Luigi Vezzoni
We consider a general class of elliptic equations on hypercomplex manifolds which includes the quaternionic Monge-Ampère equation, the quaternionic Hessian equation and the Monge-A…
The behavior of the second Ricci flow on complex parallelizable manifolds
Lucio 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 introduce…
Quasi-Kähler Chern-flat manifolds and complex 2-step nilpotent Lie algebras
Antonio J. Di Scala, Jorge Lauret, Luigi Vezzoni
The study of quasi-Kähler Chern-flat almost Hermitian manifolds is strictly related to the study of anti-bi-invariant almost complex Lie algebras. In the present paper we show that…