Nous montrons que les applications pseudo-holomorphes propres entre deux régions strictement pseudoconvexes se prolongent au bord. Le point essentiel de la démonstration est que le jacobien d'une telle application ne s'annule pas près du bord. Nous prouvons également que la régularité du prolongement dépend de la régularité des structures presque complexes, et nous obtenons des estimations explicites des normes hölderiennes. En corollaire, nous donnons dans le cas lisse une condition nécessaire et suffisante sur la structure presque complexe de l'espace d'arrivée pour que les applications pseudo-holomorphes propres se prolongent de façon lisse.
We prove that proper pseudo-holomorphic maps between strictly pseudoconvex regions in almost complex manifolds extend to the boundary. The key point is that the Jacobian of such a map is far from zero near the boundary, and the proof is mainly based on an almost complex analogue of the scaling method. We also establish the link between the regularity of the extension and the regularity of the almost complex structures, and we determine explicit estimates for the Hölderian norms. As a corollary, we get in the smooth case a necessary and sufficient condition on the almost complex structure of the target's space for the smooth extension of proper pseudo-holomorphic maps.
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Léa Blanc-Centi 1
@article{CRMATH_2007__345_8_421_0,
author = {L\'ea Blanc-Centi},
title = {R\'egularit\'e au bord des applications pseudo-holomorphes propres},
journal = {Comptes Rendus. Math\'ematique},
pages = {421--424},
publisher = {Elsevier},
volume = {345},
number = {8},
year = {2007},
doi = {10.1016/j.crma.2007.09.013},
language = {fr},
}
Léa Blanc-Centi. Régularité au bord des applications pseudo-holomorphes propres. Comptes Rendus. Mathématique, Volume 345 (2007) no. 8, pp. 421-424. doi : 10.1016/j.crma.2007.09.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.09.013/
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