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.
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
Affiliations des auteurs :
Fathi Haggui
1
;
Adel Khalfallah
1
1
Institut préparatoire aux études d'ingénieur rue Ibn-Eljazzar 5019 Monastir, Tunisie
@article{10_4064_ap101_1_6,
author = {Fathi Haggui and Adel Khalfallah},
title = {Normal pseudoholomorphic curves},
journal = {Annales Polonici Mathematici},
pages = {55--65},
year = {2011},
volume = {101},
number = {1},
doi = {10.4064/ap101-1-6},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap101-1-6/}
}
TY - JOUR
AU - Fathi Haggui
AU - Adel Khalfallah
TI - Normal pseudoholomorphic curves
JO - Annales Polonici Mathematici
PY - 2011
SP - 55
EP - 65
VL - 101
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4064/ap101-1-6/
DO - 10.4064/ap101-1-6
LA - en
ID - 10_4064_ap101_1_6
ER -
