On proper discs in complex manifolds

Drinovec Drnovšek, Barbara

doi:10.5802/aif.2304

On proper discs in complex manifolds
[Sur les disques holomorphes propres dans les variétés analytiques complexes]

Drinovec Drnovšek, Barbara ¹

¹ University of Ljubljana Institute of Mathematics, Physics and Mechanics Jadranska 19 SI-1000 Ljubljana (Slovenia)

Annales de l'Institut Fourier, Tome 57 (2007) no. 5, pp. 1521-1535.

Résumé
Abstract

Soit $X$ une variété analytique complexe de dimension au moins $2$ qui possède une fonction d’exhaustion telle que sa forme de Levi possède au moins $2$ valeurs propres strictement positives en tout point de $X$ . On construit les disques holomorphes dans $X$ par n’importe quel point donné et dans n’importe quelle direction donnée.

Let $X$ be a complex manifold of dimension at least $2$ which has an exhaustion function whose Levi form has at each point at least $2$ strictly positive eigenvalues. We construct proper holomorphic discs in $X$ through any given point and in any given direction.

DOI : 10.5802/aif.2304

Classification : 32H35, 32C25
Keywords: Complex manifolds, proper holomorphic discs
Mot clés : variété analytique complexe, disque holomorphe propre

Affiliations des auteurs :

Drinovec Drnovšek, Barbara ¹

¹ University of Ljubljana Institute of Mathematics, Physics and Mechanics Jadranska 19 SI-1000 Ljubljana (Slovenia)

@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
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/
DO  - 10.5802/aif.2304
LA  - en
ID  - AIF_2007__57_5_1521_0
ER  -

%0 Journal Article
%A Drinovec Drnovšek, Barbara
%T On proper discs in complex manifolds
%J Annales de l'Institut Fourier
%D 2007
%P 1521-1535
%V 57
%N 5
%I Association des Annales de l’institut Fourier
%U http://www.numdam.org/articles/10.5802/aif.2304/
%R 10.5802/aif.2304
%G en
%F AIF_2007__57_5_1521_0

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/

Bibliographie
Cité par

[1] Colţoiu, Mihnea $q$ -convexity. A survey, Complex analysis and geometry (Trento, 1995) (Pitman Res. Notes Math. Ser.), Volume 366, Longman, Harlow (1997), pp. 83-93 | MR | Zbl

[2] Dor, Avner A domain in $C^{m}$ not containing any proper image of the unit disc, Math. Z., Volume 222 (1996), pp. 615-625 | DOI | MR | Zbl

[3] Drinovec-Drnovšek, Barbara; Forstnerič, Franc Holomorphic curves in complex spaces (to appear in Duke Math. J.) | Zbl

[4] Forstnerič, Franc; Globevnik, Josip Discs in pseudoconvex domains, Comment. Math. Helv., Volume 67 (1992), pp. 129-145 | DOI | MR | Zbl

[5] Forstnerič, Franc; Globevnik, Josip Proper holomorphic discs in $ℂ^{2}$ , Math. Res. Lett., Volume 8 (2001), pp. 257-274 | MR | Zbl

[6] Globevnik, Josip Discs in Stein manifolds, Indiana Univ. Math. J., Volume 49 (2000), pp. 553-574 | DOI | MR | Zbl

[7] Grauert, Hans Theory of $q$ -convexity and $q$ -concavity, Several complex variables, VII (Encyclopaedia Math. Sci.), Volume 74, Springer, Berlin, 1994, pp. 259-284 | MR | Zbl

[8] Greene, Robert Everist; Wu, Hung Hsi Embedding of open Riemannian manifolds by harmonic functions, Ann. Inst. Fourier (Grenoble), Volume 25 (1975), pp. 215-235 | DOI | Numdam | MR | Zbl

[9] Henkin, Gennadi M.; Leiterer, Jürgen Andreotti-Grauert theory by integral formulas, Progress in Mathematics, 74, Birkhäuser Boston Inc., Boston, MA, 1988 | MR | Zbl

[10] Hörmander, Lars An introduction to complex analysis in several variables, North-Holland Publishing Co., Amsterdam, 1973 (North-Holland Mathematical Library, Vol. 7) | MR | Zbl

[11] Lárusson, Finnur; Sigurdsson, Ragnar Plurisubharmonic functions and analytic discs on manifolds, J. Reine Angew. Math., Volume 501 (1998), pp. 1-39 | MR | Zbl

[12] Rosay, Jean-Pierre Approximation of non-holomorphic maps, and Poletsky theory of discs, J. Korean Math. Soc., Volume 40 (2003), pp. 423-434 | DOI | MR | Zbl

[13] Rosay, Jean-Pierre Poletsky theory of disks on holomorphic manifolds, Indiana Univ. Math. J., Volume 52 (2003), pp. 157-169 | DOI | MR | Zbl

[14] Royden, H. L. The extension of regular holomorphic maps, Proc. Amer. Math. Soc., Volume 43 (1974), pp. 306-310 | DOI | MR | Zbl

[15] Rudin, Walter Real and complex analysis, McGraw-Hill Book Co., New York, 1987 | MR | Zbl

Cité par Sources :