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]
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 : https://doi.org/10.5802/aif.2562
Classification : 32Q65,  32H40
Mots clés : structure presque complexe, variété totalement réelle, disque analytique, principe de symétrie
@article{AIF_2010__60_4_1489_0,
     author = {Ivashkovich, Sergey and Sukhov, Alexandre},
     title = {Schwarz Reflection Principle, Boundary Regularity and Compactness for $J$-Complex Curves},
     journal = {Annales de l'Institut Fourier},
     pages = {1489--1513},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {60},
     number = {4},
     year = {2010},
     doi = {10.5802/aif.2562},
     mrnumber = {2722249},
     zbl = {1208.32026},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.2562/}
}
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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