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Exemples d'applications holomorphes d'indice un

Rabah Souam (1993)

Annales de l'institut Fourier

Nous construisons une famille de surfaces de Riemann hyperelliptiques, de genre variable, munies de fonctions méromorphes de degré deux et d’indice un, ce qui apporte une réponse positive à une conjecture de S. Montiel et A. Ros.

Failure of averaging on multiply connected domains

David E. Barrett (1990)

Annales de l'institut Fourier

We show that for every open Riemann surface X with non-abelian fundamental group there is a multiple-valued function f on X such that the fiberwise convex hull of the graph of f fails to contain the graph of a single-valued holomorphic function on X .

Foliations on the complex projective plane with many parabolic leaves

Marco Brunella (1994)

Annales de l'institut Fourier

We prove that a foliation on C P 2 with hyperbolic singularities and with “many" parabolic leaves (i.e. leaves without Green functions) is in fact a linear foliation. This is done in two steps: first we prove that there exists an algebraic leaf, using the technique of harmonic measures, then we show that the holonomy of this leaf is linearizable, from which the result follows easily.

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