124 citations · 2k across the 80 of their papers we have counts for
5 papers · 1 filter
Infinite time singularities of the Kähler-Ricci flow
Valentino Tosatti, Yuguang Zhang
We study the long-time behavior of the Kahler-Ricci flow on compact Kahler manifolds. We give an almost complete classification of the singularity type of the flow at infinity, dep…
The Kähler-Ricci flow, Ricci-flat metrics and collapsing limits
Valentino Tosatti, Ben Weinkove, Xiaokui Yang
We investigate the Kahler-Ricci flow on holomorphic fiber spaces whose generic fiber is a Calabi-Yau manifold. We establish uniform metric convergence to a metric on the base, away…
Remarks on the collapsing of torus fibered Calabi-Yau manifolds
Hans-Joachim Hein, Valentino Tosatti
One of the main results of the paper arXiv:1108.0967 by Gross-Tosatti-Zhang establishes estimates on the collapsing of Ricci-flat Kahler metrics on holomorphic torus fibrations. We…
estimates for nonlinear elliptic equations in complex and almost complex geometry
Valentino Tosatti, Yu Wang, Ben Weinkove +1
We describe how to use the perturbation theory of Caffarelli to prove Evans-Krylov type estimates for solutions of nonlinear elliptic equations in complex geometry, assum…
Non-Kähler Calabi-Yau manifolds
Valentino Tosatti
We study the class of compact complex manifolds whose first Chern class vanishes in the Bott-Chern cohomology. This class includes all manifolds with torsion canonical bundle, but…