124 citations · 1.4k across the 62 of their papers we have counts for
5 papers · 2 filters
Hermitian metrics, (n-1, n-1) forms and Monge-Ampère equations
Valentino Tosatti, Ben Weinkove
We show existence of unique smooth solutions to the Monge-Ampere equation for (n-1)-plurisubharmonic functions on Hermitian manifolds, generalizing previous work of the authors. As…
The degenerate J-flow and the Mabuchi energy on minimal surfaces of general type
Jian Song, Ben Weinkove
We prove existence, uniqueness and convergence of solutions of the degenerate J-flow on Kahler surfaces. As an application, we establish the properness of the Mabuchi energy for Ka…
The Monge-Ampère equation for (n-1)-plurisubharmonic functions on a compact Kähler manifold
Valentino Tosatti, Ben Weinkove
A C^2 function on C^n is called (n-1)-plurisubharmonic in the sense of Harvey-Lawson if the sum of any n-1 eigenvalues of its complex Hessian is nonnegative. We show that the assoc…
Collapsing of the Chern-Ricci flow on elliptic surfaces
Valentino Tosatti, Ben Weinkove, Xiaokui Yang
We investigate the Chern-Ricci flow, an evolution equation of Hermitian metrics generalizing the Kahler-Ricci flow, on elliptic bundles over a Riemann surface of genus greater than…
Local Calabi and curvature estimates for the Chern-Ricci flow
Morgan Sherman, Ben Weinkove
Assuming local uniform bounds on the metric for a solution of the Chern-Ricci flow, we establish local Calabi and curvature estimates using the maximum principle.