We prove the hyperbolicity of the complement of five lines in general position in an almost complex projective plane, answering a question by S. Ivashkovich.
On montre l'hyperbolicité du complémentaire de cinq droites en position générale dans un plan projectif presque complexe, répondant ainsi à une question de S. Ivashkovich.
Mot clés : hyperbolicité, théorèmes de type Picard, courbes pseudoholomorphes
Keywords: Hyperbolicity, Picard-type theorems, pseudoholomorphic curves
@article{AIF_2004__54_7_2357_0, author = {Duval, Julien}, title = {Un th\'eor\`eme de {Green} presque complexe}, journal = {Annales de l'Institut Fourier}, pages = {2357--2367}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {54}, number = {7}, year = {2004}, doi = {10.5802/aif.2082}, mrnumber = {2139696}, zbl = {1076.32020}, language = {fr}, url = {http://archive.numdam.org/articles/10.5802/aif.2082/} }
TY - JOUR AU - Duval, Julien TI - Un théorème de Green presque complexe JO - Annales de l'Institut Fourier PY - 2004 SP - 2357 EP - 2367 VL - 54 IS - 7 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2082/ DO - 10.5802/aif.2082 LA - fr ID - AIF_2004__54_7_2357_0 ER -
Duval, Julien. Un théorème de Green presque complexe. Annales de l'Institut Fourier, Volume 54 (2004) no. 7, pp. 2357-2367. doi : 10.5802/aif.2082. http://archive.numdam.org/articles/10.5802/aif.2082/
[1] Holomorphic curves in symplectic geometry, Progress in Math, 117, Birkhäuser, Basel, 1994 | MR | Zbl
[2] Sur l'hyperbolicité de certains complémentaires, Ens. Math, Volume 47 (2001), pp. 253-267 | MR | Zbl
[3] Compact manifolds and hyperbolicity, Trans. Amer. Math. Soc., Volume 235 (1978), pp. 213-219 | MR | Zbl
[4] Complete hyperbolic neighborhoods in almost-complex surfaces, Int. J. of Math, Volume 12 (2001), pp. 211-221 | DOI | MR | Zbl
[5] Some Picard theorems for holomorphic maps to algebraic varieties, Amer. J. Math., Volume 97 (1975), pp. 43-75 | DOI | MR | Zbl
[6] Pseudo holomorphic curves in symplectic manifolds, Invent. Math., Volume 82 (1985), pp. 307-347 | DOI | Zbl
[7] Hyperbolic complex spaces, Grund. der math. Wiss, 318, Springer, Berlin, 1998 | MR | Zbl
[8] Pseudoholomorphic mappings and Kobayashi hyperbolicity, Diff. Geom. Appl., Volume 11 (1999), pp. 265-277 | DOI | MR | Zbl
[9] Quasiconformal mappings in the plane, Grund. der math. Wiss, 126, Springer, Berlin, 1973 | MR | Zbl
[10] Dual elliptic planes (2000) (preprint, arXiv math.SG/0008234) | MR | Zbl
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