Normal pseudoholomorphic curves

Fathi Haggui, and Adel Khalfallah. "Normal pseudoholomorphic curves." Annales Polonici Mathematici 101.1 (2011): 55-65. <http://eudml.org/doc/281020>.

@article{FathiHaggui2011,
abstract = {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.},
author = {Fathi Haggui, Adel Khalfallah},
journal = {Annales Polonici Mathematici},
keywords = {almost complex manifolds; hyperbolic points; pseudoholomorphic curves; hyperbolically embedded submanifolds; uniformly normal families},
language = {eng},
number = {1},
pages = {55-65},
title = {Normal pseudoholomorphic curves},
url = {http://eudml.org/doc/281020},
volume = {101},
year = {2011},
}

TY - JOUR
AU - Fathi Haggui
AU - Adel Khalfallah
TI - Normal pseudoholomorphic curves
JO - Annales Polonici Mathematici
PY - 2011
VL - 101
IS - 1
SP - 55
EP - 65
AB - 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.
LA - eng
KW - almost complex manifolds; hyperbolic points; pseudoholomorphic curves; hyperbolically embedded submanifolds; uniformly normal families
UR - http://eudml.org/doc/281020
ER -