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

Ivashkovich, Sergey; Rosay, Jean-Pierre

Annales de l'Institut Fourier, Tome 54 (2004) no. 7, pp. 2387-2435.

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.

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.

Classification : 32Q60, 32Q65, 32Q45
Keywords: Kobayashi-Royden pseudo-norm, almost complex manifolds, Schwarz Lemmas, complete hyperbolicity
Mot clés : pseudo-métrique de Kobayashi-Royden, variétés presque complexes, lemmes de Schwarz, hyperbolicité complète

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