Complex Monge-Amp\`ere equations on quasi-projective varieties

We introduce generalized Monge-Amp\`ere capacities and use these to study complex Monge-Amp\`ere equations whose right-hand side is smooth outside a divisor. We prove, in many cases, that there exists a unique normalized solution which is smooth outside the divisor

Finite Pluricomplex Energy Measures

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 that this notion is a biholomorphic but not a bimeromorphic invariant

High Pt hadron-hadron correlations

We propose the formulation of a dihadron fragmentation function in terms of parton matrix elements. Under the collinear factorization approximation and facilitated by the cut-vertex technique, the two hadron inclusive cross section at leading order (LO) in e+ e- annihilation is shown to factorize into a short distance parton cross section and the long distance dihadron fragmentation function. We also derive the DGLAP evolution equation of this function at leading log. The evolution equation for the non-singlet and singlet quark fragmentation function and the gluon fragmentation function are solved numerically with the initial condition taken from event generators. Modifications to the dihadron fragmentation function from higher twist corrections in DIS off nuclei are computed. Results are presented for cases of physical interest.Comment: 7 pages, 8 figures, Latex, Proceedings of Hot Quarks 2004, July 18-24, Taos, New Mexic

Nuclear Attenuation of high energy two-hadron system in the string model

Nuclear attenuation of the two-hadron system is considered in the string model. The two-scale model and its improved version with two different choices of constituent formation time and sets of parameters obtained earlier for the single hadron attenuation, are used to describe available experimental data for the $z$-dependence of subleading hadron, whereas satisfactory agreement with the experimental data has been observed. A model prediction for $\nu$-dependence of the nuclear attenuation of the two-hadron system is also presented.Comment: 8 page

Entropy for Monge-Ampère measures in the prescribed singularities setting

In this note, we generalize the notion of entropy for potentials in a relative full Monge–Amp`ere mass E(X,θ,φ), for a model potential φ. We then investigate stability properties of this condition with respect to blow-ups and perturbation of the cohomology class. We also prove a Moser–Trudinger type inequality with general weight and we show n that functions with finite entropy lie in a relative energy class E n−1 (X, θ, φ) (provided n > 1), while they have the same singularities of φ when n = 1

H^s versus C^0-weighted minimizers

We study a class of semi-linear problems involving the fractional Laplacian under subcritical or critical growth assumptions. We prove that, for the corresponding functional, local minimizers with respect to a C^0-topology weighted with a suitable power of the distance from the boundary are actually local minimizers in the natural H^s-topology.Comment: 15 page

On the asymptotic behaviour of solutions to the fractional porous medium equation with variable density

We are concerned with the long time behaviour of solutions to the fractional porous medium equation with a variable spatial density. We prove that if the density decays slowly at infinity, then the solution approaches the Barenblatt-type solution of a proper singular fractional problem. If, on the contrary, the density decays rapidly at infinity, we show that the minimal solution multiplied by a suitable power of the time variable converges to the minimal solution of a certain fractional sublinear elliptic equation.Comment: To appear in DCDS-