Geometry of currents, intersection theory and dynamics of horizontal-like maps

We introduce a geometry on the cone of positive closed currents of bidegree (p,p) and apply it to define the intersection of such currents. We also construct and study the Green currents and the equilibrium measure for horizontal-like mappings. The Green currents satisfy some extremality properties. The equilibrium measure is invariant, mixing and has maximal entropy. It is equal to the intersection of the Green currents associated to the horizontal-like map and to its inverse.Comment: 32 pages, to appear in Ann. Inst. Fourie

On the compactification of hyperconcave ends and the theorems of Siu-Yau and Nadel

We show that the pseudoconcave holes of some naturally arising class of manifolds, called hyperconcave ends, can be filled in, including the case of complex dimension 2 . As a consequence we obtain a stronger version of the compactification theorem of Siu-Yau and extend Nadel's theorems to dimension 2.Comment: 13 pages, AMSLaTeX, short version accepted for publication in Inventiones Mat