[Sur les disques holomorphes propres dans les variétés analytiques complexes]
Soit une variété analytique complexe de dimension au moins qui possède une fonction d’exhaustion telle que sa forme de Levi possède au moins valeurs propres strictement positives en tout point de . On construit les disques holomorphes dans par n’importe quel point donné et dans n’importe quelle direction donnée.
Let be a complex manifold of dimension at least which has an exhaustion function whose Levi form has at each point at least strictly positive eigenvalues. We construct proper holomorphic discs in through any given point and in any given direction.
Classification : 32H35, 32C25
Mots clés : variété analytique complexe, disque holomorphe propre
@article{AIF_2007__57_5_1521_0,
author = {Drinovec~Drnov\v{s}ek, Barbara},
title = {On proper discs in complex manifolds},
journal = {Annales de l'Institut Fourier},
pages = {1521--1535},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {57},
number = {5},
year = {2007},
doi = {10.5802/aif.2304},
mrnumber = {2364140},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.2304/}
}
TY - JOUR AU - Drinovec Drnovšek, Barbara TI - On proper discs in complex manifolds JO - Annales de l'Institut Fourier PY - 2007 DA - 2007/// SP - 1521 EP - 1535 VL - 57 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2304/ UR - https://www.ams.org/mathscinet-getitem?mr=2364140 UR - https://doi.org/10.5802/aif.2304 DO - 10.5802/aif.2304 LA - en ID - AIF_2007__57_5_1521_0 ER -
Drinovec Drnovšek, Barbara. On proper discs in complex manifolds. Annales de l'Institut Fourier, Tome 57 (2007) no. 5, pp. 1521-1535. doi : 10.5802/aif.2304. http://www.numdam.org/articles/10.5802/aif.2304/
[1] -convexity. A survey, Complex analysis and geometry (Trento, 1995) (Pitman Res. Notes Math. Ser.), Volume 366 (1997), pp. 83-93 | MR 1477441 | Zbl 0883.32016
[2] A domain in not containing any proper image of the unit disc, Math. Z., Volume 222 (1996), pp. 615-625 | Article | MR 1406270 | Zbl 0864.32018
[3] Holomorphic curves in complex spaces (to appear in Duke Math. J.) | Zbl 1133.32002
[4] Discs in pseudoconvex domains, Comment. Math. Helv., Volume 67 (1992), pp. 129-145 | Article | MR 1144617 | Zbl 0779.32016
[5] Proper holomorphic discs in , Math. Res. Lett., Volume 8 (2001), pp. 257-274 | MR 1839476 | Zbl 1027.32018
[6] Discs in Stein manifolds, Indiana Univ. Math. J., Volume 49 (2000), pp. 553-574 | Article | MR 1793682 | Zbl 0974.32017
[7] Theory of -convexity and -concavity, Several complex variables, VII (Encyclopaedia Math. Sci.), Volume 74, Springer, Berlin, 1994, pp. 259-284 | MR 1326623 | Zbl 0806.32004
[8] Embedding of open Riemannian manifolds by harmonic functions, Ann. Inst. Fourier (Grenoble), Volume 25 (1975), pp. 215-235 | Article | Numdam | MR 382701 | Zbl 0307.31003
[9] Andreotti-Grauert theory by integral formulas, Progress in Mathematics, 74, Birkhäuser Boston Inc., Boston, MA, 1988 | MR 986248 | Zbl 0654.32002
[10] An introduction to complex analysis in several variables, North-Holland Publishing Co., Amsterdam, 1973 (North-Holland Mathematical Library, Vol. 7) | MR 344507 | Zbl 0271.32001
[11] Plurisubharmonic functions and analytic discs on manifolds, J. Reine Angew. Math., Volume 501 (1998), pp. 1-39 | MR 1637837 | Zbl 0901.31004
[12] Approximation of non-holomorphic maps, and Poletsky theory of discs, J. Korean Math. Soc., Volume 40 (2003), pp. 423-434 | Article | MR 1973910 | Zbl 1040.32015
[13] Poletsky theory of disks on holomorphic manifolds, Indiana Univ. Math. J., Volume 52 (2003), pp. 157-169 | Article | MR 1970025 | Zbl 1033.31006
[14] The extension of regular holomorphic maps, Proc. Amer. Math. Soc., Volume 43 (1974), pp. 306-310 | Article | MR 335851 | Zbl 0292.32019
[15] Real and complex analysis, McGraw-Hill Book Co., New York, 1987 | MR 924157 | Zbl 0925.00005
Cité par Sources :
