124 citations · 2k across the 80 of their papers we have counts for
6 papers · 1 filter
On the regularity of geodesics in the space of Kähler metrics
Jianchun Chu, Valentino Tosatti, Ben Weinkove
We prove that any two Kahler potentials on a compact Kahler manifold can be connected by a geodesic segment of C^{1,1} regularity. This follows from an a priori interior real Hessi…
Restricted volumes on Kähler manifolds
Tristan C. Collins, Valentino Tosatti
We study numerical restricted volumes of (1,1) classes on compact Kahler manifolds, as introduced by Boucksom. Inspired by work of Ein-Lazarsfeld-Mustata-Nakamaye-Popa on restricte…
The Aleksandrov-Bakelman-Pucci estimate and the Calabi-Yau equation
Valentino Tosatti, Ben Weinkove
We give two applications of the Aleksandrov-Bakelman-Pucci estimate to the Calabi-Yau equation on symplectic four-manifolds. The first is solvability of the equation on the Kodaira…
Orthogonality of divisorial Zariski decompositions for classes with volume zero
Valentino Tosatti
We show that the orthogonality conjecture for divisorial Zariski decompositions on compact Kahler manifolds holds for pseudoeffective (1,1) classes with volume zero.
The Monge-Ampère equation for non-integrable almost complex structures
Jianchun Chu, Valentino Tosatti, Ben Weinkove
We show existence and uniqueness of solutions to the Monge-Ampere equation on compact almost complex manifolds with non-integrable almost complex structure.
Nakamaye's theorem on complex manifolds
Valentino Tosatti
We discuss Nakamaye's Theorem and its recent extension to compact complex manifolds, together with some applications.