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
We establish the Schwarz Reflection Principle for
Keywords: Almost complex structure, totally real manifold, holomorphic disc, reflection principle
Mot 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}, zbl = {1208.32026}, mrnumber = {2722249}, language = {en}, url = {https://www.numdam.org/articles/10.5802/aif.2562/} }
TY - JOUR AU - Ivashkovich, Sergey AU - Sukhov, Alexandre TI - Schwarz Reflection Principle, Boundary Regularity and Compactness for $J$-Complex Curves JO - Annales de l'Institut Fourier PY - 2010 SP - 1489 EP - 1513 VL - 60 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://www.numdam.org/articles/10.5802/aif.2562/ DO - 10.5802/aif.2562 LA - en ID - AIF_2010__60_4_1489_0 ER -
%0 Journal Article %A Ivashkovich, Sergey %A Sukhov, Alexandre %T Schwarz Reflection Principle, Boundary Regularity and Compactness for $J$-Complex Curves %J Annales de l'Institut Fourier %D 2010 %P 1489-1513 %V 60 %N 4 %I Association des Annales de l’institut Fourier %U https://www.numdam.org/articles/10.5802/aif.2562/ %R 10.5802/aif.2562 %G en %F 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, Tome 60 (2010) no. 4, pp. 1489-1513. doi : 10.5802/aif.2562. https://www.numdam.org/articles/10.5802/aif.2562/
[1] Continuing
[2] Partial differential equations, J. Wiley and Sons, 1964 | MR | Zbl
[3] Zum Schwarzschen Spiegelungsprinzip, Comm. Math. Helv., Volume 19 (1946) no. 1, pp. 263-278 | DOI | MR
[4] Regularity of boundaries of analytic sets, Math. USSR Sbornik, Volume 43 (1983), pp. 291-335 | DOI | MR | Zbl
[5] Fefferman’s mapping theorem on almost complex manifold in complex dimension two, Math. Z., Volume 250 (2005), pp. 59-90 | DOI | MR | Zbl
[6] Gromov Compactness in Hölder Spaces and Minimal Connections on Jet Bundles, math. SG/0808.0415
[7] On the geometry of model almost complex manifolds with boundary, Math. Z., Volume 254 (2006), pp. 567-589 | DOI | MR | Zbl
[8] Schwarz-type lemmas for solutions of
[9] Gromov Compactness Theorem for
[10] Reflection Principle and
[11] The tangent bundle of an almost complex manifold, Canad. Math. Bull., Volume 44 (2001), pp. 70-79 | DOI | MR | Zbl
[12]
[13] Boundary-value problems with free boundary for elliptic systems of equations, Translations of Mathematical Monographs, 57, AMS, Providence, RI, 1983 522 pp. (Originally published by Nauka, Novosibirsk, 1977) | MR | Zbl
[14] Multiple integrals in the calculus of variations, Springer Verlag, 1966 | MR | Zbl
[15] Über einige Abbildungsaufgaben, Journal für reine und angewandte Mathematik, Volume 70 (1869), p. 105-120 (see pages 106–107) See also Gesammelte mathematische Abhandlungen, Springer (1892), 66-67. Or the Second Edition, Bronx, N.Y., Chelsea Pub. Co. (1972) | DOI
[16] Some properties of holomorphic curves in almost complex manifolds, Holomorphic curves in symplectic geometry (Progress in Mathematics), Volume 117, Birkhäuser, 1994, pp. 165-189 (Ch. V) | MR
[17] Theory of Function Spaces, Birkhäuser, 1983 | MR
[18] Generalized analytic functions, Fizmatgiz, Moscow, 1959 English translation - Pergamon Press, London, and Addison-Welsey, Reading, Massachusetts (1962) | MR | Zbl
[19] Tangent and cotangent bundles, Marcel Dekker, NY, 1973 | MR | Zbl
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