Harmonic Currents of Finite Energy and Laminations

Details Harmonic Currents of Finite Energy and Laminations Harmonic Currents of Finite Energy and Laminations

2004-02-26

arxiv.org/abs/math/0402432v1

Mathematics

Complex Variables

29 pages

Scientific paper

We introduce, on a complex Kahler manifold (M,\omega), 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.

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