Sur les automorphismes analytiques des variétés hyperboliques |
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Authors: | Jean-Jacques Loeb Jean-Pierre Vigué |
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Institution: | a UMR 6093, Université d'Angers, Département de Mathématiques, Mathématiques, 2 Bd Lavoisier, 49045 Angers Cedex 01, France b UMR CNRS 6086, Université de Poitiers, Mathématiques, SP2MI, BP 30179, 86962 FUTUROSCOPE, France |
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Abstract: | Results of H. Cartan about holomorphic automorphisms on bounded domains are generalized to the case of hyperbolic manifolds in the sense of Kobayashi. In this setting, we give an identity theorem together with its topological version. We show also that a sequence of automorphisms which converges uniformly on some nonempty open set, has a limit on the whole space which is an automorphism. At the end of the paper, conditions are given for the sequence of iterates of a self holomorphic map in order to be an automorphism. |
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Keywords: | primary 32Q45 secondary 32H02 32H50 |
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