Schwarz Reflection Principle, Boundary Regularity and Compactness for J -Complex Curves

Sergey Ivashkovich[1]; Alexandre Sukhov[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)

Annales de l’institut Fourier (2010)

  • Volume: 60, Issue: 4, page 1489-1513
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Ivashkovich, Sergey, and Sukhov, Alexandre. "Schwarz Reflection Principle, Boundary Regularity and Compactness for $J$-Complex Curves." Annales de l’institut Fourier 60.4 (2010): 1489-1513. <http://eudml.org/doc/116311>.

@article{Ivashkovich2010,
abstract = {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 $\mathcal\{C\}^\{k,\alpha \}$-classes.},
affiliation = {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); U.F.R. de Mathématiques Université de Lille-1 59655 Villeneuve d’Ascq (France)},
author = {Ivashkovich, Sergey, Sukhov, Alexandre},
journal = {Annales de l’institut Fourier},
keywords = {Almost complex structure; totally real manifold; holomorphic disc; reflection principle; almost complex structure},
language = {eng},
number = {4},
pages = {1489-1513},
publisher = {Association des Annales de l’institut Fourier},
title = {Schwarz Reflection Principle, Boundary Regularity and Compactness for $J$-Complex Curves},
url = {http://eudml.org/doc/116311},
volume = {60},
year = {2010},
}

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
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 4
SP - 1489
EP - 1513
AB - 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 $\mathcal{C}^{k,\alpha }$-classes.
LA - eng
KW - Almost complex structure; totally real manifold; holomorphic disc; reflection principle; almost complex structure
UR - http://eudml.org/doc/116311
ER -

References

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