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)

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     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},
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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://archive.numdam.org/articles/10.5802/aif.2304/

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