3 papers
math.DG2024
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…
math.DG2022
Fully non-linear elliptic equations on compact hyperhermitian manifolds with a flat hyperkähler metric
Giovanni Gentili
Mainly motivated by a conjecture of Alesker and Verbitsky, we study a class of elliptic equations on compact hyperhermitian manifolds. By adapting the approach of Székelyhidi to th…
math.DG2020
The quaternionic Calabi conjecture on abelian hypercomplex nilmanifolds viewed as tori fibrations
Giovanni Gentili, Luigi Vezzoni
We study the quaternionic Calabi-Yau problem in HKT geometry introduced by Alesker and Verbitsky on 8-dimensional 2-step nilmanifolds with an abelian hypercomplex structure. We sho…