Harmonic Currents of Finite Energy and Laminations

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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 $\int T \wedge T \wedge ω^{k-2},$ 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

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Complex Variables, Dynamical Systems

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http://salesiana.dossiersoluciones.com/handle/123456789/70287

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0402432
 http://arxiv.org/abs/math/0402432

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arXiv