Normal pseudoholomorphic curves

Fathi Haggui¹ ; Adel Khalfallah¹

¹ Institut préparatoire aux études d'ingénieur rue Ibn-Eljazzar 5019 Monastir, Tunisie

Annales Polonici Mathematici, Tome 101 (2011) no. 1, pp. 55-65

Résumé

First, we give some characterizations of $J$-hyperbolic points for almost complex manifolds. We apply these characterizations to show that the hyperbolic embeddedness of an almost complex submanifold follows from relative compactness of certain spaces of continuous extensions of pseudoholomorphic curves defined on the punctured unit disc. Next, we define uniformly normal families of pseudoholomorphic curves. We prove extension-convergence theorems for these families similar to those obtained by Kobayashi, Kiernan and Joseph–Kwack in the standard complex case.

Détail

DOI : 10.4064/ap101-1-6

Keywords: first characterizations j hyperbolic points almost complex manifolds apply these characterizations hyperbolic embeddedness almost complex submanifold follows relative compactness certain spaces continuous extensions pseudoholomorphic curves defined punctured unit disc define uniformly normal families pseudoholomorphic curves prove extension convergence theorems these families similar those obtained kobayashi kiernan joseph kwack standard complex