Regularization of currents and entropy

Abstract

Let T be a positive closed (p,p)-current of mass 1 on a compact Kahler manifold X. Then, there exist a constant c, independent of T, and smooth positive closed (p,p)-currents Tn and Sn of mass c such that Tn-Sn converge weakly to T. We also extend this result to positive pluriharmonic currents. Then we study the wedge product of positive closed (1,1)-currents having continuous potential with positive pluriharmonic currents. As an application, we give an estimate of the topological entropy of meromorphic maps on compact Kahler manifolds.