no. 4
Schwarz Reflection Principle, Boundary Regularity and Compactness for J-Complex Curves
[Principe de symétrie de Schwarz, régularité au bord et compacité pour les courbes J-complexes]
Ivashkovich, Sergey1 ; Sukhov, Alexandre2
1 U.F.R. de Mathématiques Université de Lille-1 59655 Villeneuve d’Ascq (France) and IAPMM Acad. Sci. Ukraine Lviv, Naukova 3b, 79601 Ukraine (Ukraine)
2 U.F.R. de Mathématiques Université de Lille-1 59655 Villeneuve d’Ascq (France)
Annales de l'Institut Fourier, Tome 60 (2010) no. 4, pp. 1489-1513.

Nous établissons le Principe de Symétrie de Schwarz pour les disques complexes attachés à une sous-variété analytique réelle et totalement réelle d’une variété presque complexe munie d’une structure presque complexe analytique réelle. Nous prouvons également la régularité au bord précise de ces disques et nous en déduisons la convergence exacte dans le théorème de compacité de Gromov dans les classes 𝒞 k,α .

We establish the Schwarz Reflection Principle for J-complex discs attached to a real analytic J-totally real submanifold of an almost complex manifold with real analytic J. We also prove the precise boundary regularity and derive the precise convergence in Gromov compactness theorem in 𝒞 k,α -classes.

DOI : 10.5802/aif.2562
Classification : 32Q65, 32H40
Keywords: Almost complex structure, totally real manifold, holomorphic disc, reflection principle
Mot clés : structure presque complexe, variété totalement réelle, disque analytique, principe de symétrie
Ivashkovich, Sergey 1 ; Sukhov, Alexandre 2

1 U.F.R. de Mathématiques Université de Lille-1 59655 Villeneuve d’Ascq (France) and IAPMM Acad. Sci. Ukraine Lviv, Naukova 3b, 79601 Ukraine (Ukraine)
2 U.F.R. de Mathématiques Université de Lille-1 59655 Villeneuve d’Ascq (France) 
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     title = {Schwarz {Reflection} {Principle,} {Boundary} {Regularity} and {Compactness} for $J${-Complex} {Curves}},
     journal = {Annales de l'Institut Fourier},
     pages = {1489--1513},
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Ivashkovich, Sergey; Sukhov, Alexandre. Schwarz Reflection Principle, Boundary Regularity and Compactness for $J$-Complex Curves. Annales de l'Institut Fourier, Tome 60 (2010) no. 4, pp. 1489-1513. doi : 10.5802/aif.2562. http://www.numdam.org/articles/10.5802/aif.2562/

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