no. 4
Uniformization of the leaves of a rational vector field
Annales de l'Institut Fourier, Tome 45 (1995) no. 4, pp. 1123-1133.

Nous étudions la structure analytique des feuilles d’un feuilletage holomorphe par des courbes dans une variété complexe. Nous montrons que si chaque feuille est une surface hyperbolique, alors l’application d’uniformisation est continue. Dans le cas de l’espace projectif complexe il suffit qu’il n’y ait pas de feuille algébrique.

We study the analytic structure of the leaves of a holomorphic foliation by curves on a compact complex manifold. We show that if every leaf is a hyperbolic surface then they can be simultaneously uniformized in a continuous manner. In case the manifold is complex projective space a sufficient condition is that there are no algebraic leaf.

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     title = {Uniformization of the leaves of a rational vector field},
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Candel, Alberto; Gómez-Mont, X. Uniformization of the leaves of a rational vector field. Annales de l'Institut Fourier, Tome 45 (1995) no. 4, pp. 1123-1133. doi : 10.5802/aif.1488. http://www.numdam.org/articles/10.5802/aif.1488/

[1]L. Ahlfors, Complex Analysis, MacGraw Hill, New York, 1966. | Zbl

[2]L. Ahlfors, Conformal Invariants, MacGraw Hill, New York, 1973.

[3]R. Brody, Compact manifolds and hyperbolicity, Trans. Amer. Math. Soc., 235 (1978), 213-219. | MR | Zbl

[4]C. Camacho, A. Lins, P. Sad, Minimal sets of foliations on complex projective spaces, Publ. Math. IHES, 68 (1989), 187-203. | Numdam | Zbl

[5]A. Candel, Uniformization of surface laminations, Ann. Scient. Ec. Norm. Sup., 26 (1993), 489-516. | Numdam | MR | Zbl

[6]D. Cerveau, Equations différentielles algébriques : Remarques et problèmes, J. Fac. Sci. Univ. Tokyo, 36 (1989), 665-680. | MR | Zbl

[7]E. Ghys, Gauss-Bonnet Theorem for 2-dimensional foliations, J. of Funct. Anal., 77 (1988), 51-59. | MR | Zbl

[8]A.A. Glutsuk, The hyperbolicity of phase curves of a generic polynomial vector field in Cn, Functional Analysis and its applications, 28 (1994), 77-84. | Zbl

[9]A. Lins, Simultaneous uniformization for the leaves of projective foliations by curves, to appear in Bol. Soc. Brasileira. | Zbl

[10]C. Moore &Amp; C. Schochet, Global analysis of foliated spaces, Springer-Verlag, New York, 1988. | Zbl

[11]A. Verjovsky, A uniformization theorem for holomorphic foliations., Contemp. Math., 58(III) (1987), 233-253. | MR | Zbl

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