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.
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.
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
Ivashkovich, Sergey 1; Rosay, Jean-Pierre 
@article{AIF_2004__54_7_2387_0, author = {Ivashkovich, Sergey and Rosay, Jean-Pierre}, title = {Schwarz-type lemmas for solutions of $\bar{\partial }$-inequalities and complete hyperbolicity of almost complex manifolds}, journal = {Annales de l'Institut Fourier}, pages = {2387--2435}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {54}, number = {7}, year = {2004}, doi = {10.5802/aif.2084}, zbl = {1072.32007}, mrnumber = {2139698}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2084/} }
TY - JOUR AU - Ivashkovich, Sergey AU - Rosay, Jean-Pierre TI - Schwarz-type lemmas for solutions of $\bar{\partial }$-inequalities and complete hyperbolicity of almost complex manifolds JO - Annales de l'Institut Fourier PY - 2004 SP - 2387 EP - 2435 VL - 54 IS - 7 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2084/ DO - 10.5802/aif.2084 LA - en ID - AIF_2004__54_7_2387_0 ER -
%0 Journal Article %A Ivashkovich, Sergey %A Rosay, Jean-Pierre %T Schwarz-type lemmas for solutions of $\bar{\partial }$-inequalities and complete hyperbolicity of almost complex manifolds %J Annales de l'Institut Fourier %D 2004 %P 2387-2435 %V 54 %N 7 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2084/ %R 10.5802/aif.2084 %G en %F AIF_2004__54_7_2387_0
Ivashkovich, Sergey; Rosay, Jean-Pierre. Schwarz-type lemmas for solutions of $\bar{\partial }$-inequalities and complete hyperbolicity of almost complex manifolds. Annales de l'Institut Fourier, Volume 54 (2004) no. 7, pp. 2387-2435. doi : 10.5802/aif.2084. https://aif.centre-mersenne.org/articles/10.5802/aif.2084/
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