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math.DG2010★ 14 cited
Degenerations of Calabi-Yau metrics
Valentino Tosatti
This is a survey of our recent work on degenerations of Ricci-flat Kahler metrics on compact Calabi-Yau manifolds with Kahler classes approaching the boundary of the Kahler cone.
math.DG2007★ 88 cited
Taming symplectic forms and the Calabi-Yau equation
Valentino Tosatti, Ben Weinkove, Shing-Tung Yau
We study the Calabi-Yau equation on symplectic manifolds. We show that Donaldson's conjecture on estimates for this equation in terms of a taming symplectic form can be reduced to…
math.DG2005
On the Critical Points of the E_k Functionals in Kahler Geometry
Valentino Tosatti
We prove that a Kahler metric in the anticanonical class which is a critical point of the functional E_k and has nonnegative Ricci curvature, is necessarily Kahler-Einstein. This p…