61 citations · 205 across the 11 of their papers we have counts for
15 papers
Relative pluripotential theory on compact Kähler manifolds
Tamás Darvas, Eleonora Di Nezza, Chinh H. Lu
Given a compact Kähler manifold, we survey the study of complex Monge-Ampère type equations with prescribed singularity type, developed by the authors in a series of papers. In add…
The Regularity of Envelopes
Eleonora Di Nezza, Stefano Trapani
Let be a compact complex manifold of complex dimension and be a smooth closed real form on such that its cohomology class is big.…
Families of singular Kähler-Einstein metrics
Eleonora Di Nezza, Vincent Guedj, Henri Guenancia
Refining Yau's and Kolodziej's techniques, we establish very precise uniform a priori estimates for degenerate complex Monge-Ampère equations on compact Kähler manifolds, that allo…
The metric geometry of singularity types
Tamás Darvas, Eleonora Di Nezza, Chinh H. Lu
Let be a compact Kähler manifold. Given a big cohomology class , there is a natural equivalence relation on the space of -psh functions giving rise to $\mathcal S(X,θ…
Log-concavity of volume and complex Monge-Ampère equations with prescribed singularity
Tamás Darvas, Eleonora Di Nezza, Chinh H. Lu
Let be a compact Kähler manifold. We prove the existence and uniqueness of solutions to complex Monge-Ampère equations with prescribed singularity type. Compared to previou…
L^1 metric geometry of big cohomology classes
Tamás Darvas, Eleonora Di Nezza, Chinh H. Lu
Suppose is a compact Kähler manifold of dimension , and is closed -form representing a big cohomology class. We introduce a metric on the finite energy…
Monotonicity of non-pluripolar products and complex Monge-Ampère equations with prescribed singularity
Tamás Darvas, Eleonora Di Nezza, Chinh H. Lu
We establish the monotonicity property for the mass of non-pluripolar products on compact Kahler manifolds, and we initiate the study of complex Monge-Ampere type equations with pr…
Geometry and Topology of the space of Kähler metrics on singular varieties
Eleonora Di Nezza, Vincent Guedj
Let be a compact Kähler normal space and a Kähler class. We study metric properties of the space of Kähler metrics in using Mab…
On the singularity type of full mass currents in big cohomology classes
Tamás Darvas, Eleonora Di Nezza, Chinh H. Lu
Let be a compact Kähler manifold and be a big cohomology class. We prove several results about the singularity type of full mass currents, answering a number of open qu…
Finite Pluricomplex energy measures
Eleonora Di Nezza
We investigate probability measures with finite pluricomplex energy. We give criteria insuring that a given measure has finite energy and test these on various examples. We show th…
Uniqueness and short time regularity of the weak Kähler-Ricci flow
Eleonora Di Nezza, Chinh H. Lu
Let be a compact Kähler manifold. We prove that the Kähler-Ricci flow starting from arbitrary closed positive -currents is smooth outside some analytic subset. This regu…
Generalized Monge-Ampère capacities
Eleonora Di Nezza, Chinh H. Lu
We study various capacities on compact Kähler manifolds which generalize the Bedford-Taylor Monge-Ampère capacity. We then use these capacities to study the existence and the regul…
Complex Monge-Ampère equations on quasi-projective varieties
Eleonora Di Nezza, Chinh H. Lu
We introduce generalized Monge-Ampère capacities and use these to study complex Monge-Ampère equations whose right-hand side is smooth outside a divisor. We prove, in many cases, t…
Stability of Monge-Ampère energy classes
Eleonora Di Nezza
We show that the non pluripolar product of positive currents is a bimeromorphic invariant. Under some natural assumptions, we show that the (weighted) energy associated to big coho…
Hitchhiker's guide to the fractional Sobolev spaces
Eleonora Di Nezza, Giampiero Palatucci, Enrico Valdinoci
This paper deals with the fractional Sobolev spaces W^[s,p]. We analyze the relations among some of their possible definitions and their role in the trace theory. We prove continuo…