Harmonic Currents of Finite Energy and Laminations

Abstract

We introduce, on a complex Kahler manifold (M,ω), a notion of energy for harmonic currents of bidegree (1,1). This allows us to define $\int T\wedge T\wedge {\omega }^{k-2},$ for positive harmonic currents. We then show that for a lamination with singularities of a compact set in P^2 there is a unique positive harmonic current which minimizes energy. If X is a compact laminated set in P^2 of class C^1 it carries a unique positive harmonic current T of mass 1. The current T can be obtained by an Ahlfors type construction starting with a arbitrary leaf of X.

29 pages