124 citations · 2k across the 80 of their papers we have counts for
6 papers · 1 filter
Regularity of weak solutions of a complex Monge-Ampère equation
Gábor Székelyhidi, Valentino Tosatti
We prove the smoothness of weak solutions to an elliptic complex Monge-Ampere equation, using the smoothing property of the corresponding parabolic flow.
The complex Monge-Ampère equation on compact Hermitian manifolds
Valentino Tosatti, Ben Weinkove
We show that, up to scaling, the complex Monge-Ampere equation on compact Hermitian manifolds always admits a smooth solution.
Estimates for the complex Monge-Ampère equation on Hermitian and balanced manifolds
Valentino Tosatti, Ben Weinkove
We generalize Yau's estimates for the complex Monge-Ampere equation on compact manifolds in the case when the background metric is no longer Kahler. We prove a priori…
The Calabi-Yau equation on the Kodaira-Thurston manifold
Valentino Tosatti, Ben Weinkove
We prove that the Calabi-Yau equation can be solved on the Kodaira-Thurston manifold for all given -invariant volume forms. This provides support for Donaldson's conjecture th…
Adiabatic limits of Ricci-flat Kahler metrics
Valentino Tosatti
We study adiabatic limits of Ricci-flat Kahler metrics on a Calabi-Yau manifold which is the total space of a holomorphic fibration when the volume of the fibers goes to zero. By e…
The Calabi-Yau equation, symplectic forms and almost complex structures
Valentino Tosatti, Ben Weinkove
We discuss a conjecture of Donaldson on a version of Yau's Theorem for symplectic forms with compatible almost complex structures and survey some recent progress on this problem. W…