Applications harmoniques et hyperbolicité des domaines tubes

2006/10/26 by J-J. Loeb, Loeb, J-J.
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals #math.CV #msc:32A07

paper · pdf · doi:10.48550/arxiv.math/0610796

arxiv created 2006/10/26 · arxiv updated 2009/12/01

Abstract

An application of the Zalcman renormalization theorem to harmonic functions shows that the limit functions are nonconstant affine. Extensions of this method are given for maps with values in a torus or in a complex Lie groups. As an application, we give criteria of Kobayashi hyperbolicity for tubes in \Bbb C².

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