Schwarz-type lemmas for solutions of $\bar{\partial }$-inequalities and complete hyperbolicity of almost complex manifolds

[Lemmes du type Lemme de Schwarz pour les solutions d’ inégalités différentielles pour $\overline{\partial }$ et hyperbolicité complète de variétés presque complexes]

Ivashkovich, Sergey ; Rosay, Jean-Pierre

Annales de l'Institut Fourier, Tome 54 (2004), p. 2387-2435 / Harvested from Numdam

Résumé

La pseudo-métrique de Kobayashi-Royden est définie pour les variétés presque complexes de façon similaire au cas complexe. Nous étudions quels domaines sont complets pour cette métrique, en particulier nous étudions le complément de sous variétés de co-dimension 1 ou 2. Le papier inclut une discussion, avec preuves, de faits à la base de la théorie des disques pseudo-holomorphes.

Abstract

The definition of the Kobayashi-Royden pseudo-metric for almost complex manifolds is similar to its definition for complex manifolds. We study the question of completeness of some domains for this metric. In particular, we study the completeness of the complement of submanifolds of co-dimension 1 or 2. The paper includes a discussion, with proofs, of basic facts in the theory of pseudo-holomorphic discs.

Détail

Publié le : 2004-01-01

MR 2139698 | Zbl 1072.32007 | 5 citations dans Numdam

DOI : https://doi.org/10.5802/aif.2084
Classification:  32Q60,  32Q65,  32Q45
Mots clés: pseudo-métrique de Kobayashi-Royden, variétés presque complexes, lemmes de Schwarz, hyperbolicité complète

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