124 citations · 1.4k across the 62 of their papers we have counts for
5 papers · 2 filters
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…
The Kähler-Ricci flow on Hirzebruch surfaces
Jian Song, Ben Weinkove
We investigate the metric behavior of the Kahler-Ricci flow on the Hirzebruch surfaces, assuming the initial metric is invariant under a maximal compact subgroup of the automorphis…
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…