Schwarz Reflection Principle, Boundary Regularity and Compactness for J-Complex Curves
Annales de l'Institut Fourier, Volume 60 (2010) no. 4, p. 1489-1513

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.

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 .

DOI : https://doi.org/10.5802/aif.2562
Classification:  32Q65,  32H40
Keywords: Almost complex structure, totally real manifold, holomorphic disc, reflection principle
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {60},
     number = {4},
     year = {2010},
     pages = {1489-1513},
     doi = {10.5802/aif.2562},
     mrnumber = {2722249},
     zbl = {1208.32026},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2010__60_4_1489_0}
}
Ivashkovich, Sergey; Sukhov, Alexandre. Schwarz Reflection Principle, Boundary Regularity and Compactness for $J$-Complex Curves. Annales de l'Institut Fourier, Volume 60 (2010) no. 4, pp. 1489-1513. doi : 10.5802/aif.2562. http://www.numdam.org/item/AIF_2010__60_4_1489_0/

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