18 citations · 40 across the 35 of their papers we have counts for
6 papers · 1 filter
Complex Monge-Ampere equations with solutions in finite energy classes
Do Duc Thai, Duc-Viet Vu
We characterize the class of probability measures on a compact Kahler manifold such that the associated Monge-Ampère equation has a solution of finite pluricomplex energy. Our resu…
Lelong numbers of currents of full mass intersection
Duc-Viet Vu
We study Lelong numbers of currents of full mass intersection on a compact Kaehler manifold in a mixed setting. Our main theorems cover some recent results due to Darvas-Di Nezza-L…
Density currents and relative non-pluripolar products
Duc-Viet Vu
We compare the notion of relative non-pluripolar products and that of density currents on compact Kahler manifolds.
Moser-Trudinger inequalities and complex Monge-Ampere equation
Tien-Cuong Dinh, George Marinescu, Duc-Viet Vu
Our aim is to give a version of the Moser-Trudinger inequality in the setting of complex geometry. As a very particular case, our result already gives a new Moser-Trudinger inequal…
Convexity of the class of currents with finite relative energy
Duc-Viet Vu
We prove the convexity of the class of currents with finite relative energy. A key ingredient is an integration by parts formula for relative non-pluripolar products which is of in…
Intersection of (1,1)-currents and the domain of definition of the Monge-Ampere operator
Dinh Tuan Huynh, Lucas Kaufmann, Duc-Viet Vu
We study the Monge-Amp\` ere operator within the framework of Dinh-Sibony's intersection theory defined via density currents. We show that if is a plurisubharmonic function bel…