Partial indices of analytic discs attached to lagrangian submanifolds of ℂ N

Josip Globevnik

Annales de l'institut Fourier (1996)

  • Volume: 46, Issue: 5, page 1307-1326
  • ISSN: 0373-0956

Abstract

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Integers κ 1 , ... , κ N are the partial indices of an analytic disc attached to a maximally real submanifolds of ℂ N if and only if κ j ≥ 2 for at least one j . If this is the case there are a Lagrangian submanifold M of ℂ N and an analytic disc attached to M with partial indices κ 1 , ... , κ N .

How to cite

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Globevnik, Josip. "Partial indices of analytic discs attached to lagrangian submanifolds of ${\mathbb {C}}^N$." Annales de l'institut Fourier 46.5 (1996): 1307-1326. <http://eudml.org/doc/75214>.

@article{Globevnik1996,
abstract = {Integers $\kappa _1,\ldots \{\},\kappa _N$ are the partial indices of an analytic disc attached to a maximally real submanifolds of $\{\Bbb C\}^N$ if and only if $\kappa _j\ge 2$ for at least one $j$. If this is the case there are a Lagrangian submanifold $M$ of $\{\Bbb C\}^N$ and an analytic disc attached to $M$ with partial indices $\kappa ^1,\ldots \{\},\kappa ^N$.},
author = {Globevnik, Josip},
journal = {Annales de l'institut Fourier},
keywords = {analytic disc; maximally real submanifold; Lagrangian submanifold},
language = {eng},
number = {5},
pages = {1307-1326},
publisher = {Association des Annales de l'Institut Fourier},
title = {Partial indices of analytic discs attached to lagrangian submanifolds of $\{\mathbb \{C\}\}^N$},
url = {http://eudml.org/doc/75214},
volume = {46},
year = {1996},
}

TY - JOUR
AU - Globevnik, Josip
TI - Partial indices of analytic discs attached to lagrangian submanifolds of ${\mathbb {C}}^N$
JO - Annales de l'institut Fourier
PY - 1996
PB - Association des Annales de l'Institut Fourier
VL - 46
IS - 5
SP - 1307
EP - 1326
AB - Integers $\kappa _1,\ldots {},\kappa _N$ are the partial indices of an analytic disc attached to a maximally real submanifolds of ${\Bbb C}^N$ if and only if $\kappa _j\ge 2$ for at least one $j$. If this is the case there are a Lagrangian submanifold $M$ of ${\Bbb C}^N$ and an analytic disc attached to $M$ with partial indices $\kappa ^1,\ldots {},\kappa ^N$.
LA - eng
KW - analytic disc; maximally real submanifold; Lagrangian submanifold
UR - http://eudml.org/doc/75214
ER -

References

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  2. [Č1] M. ČERNE, Minimal discs with free boundaries in a Lagrangian submanifold of ℂn, Indiana Univ. Math. J., 44 (1995), 153-164. Zbl1010.58500MR96f:58035
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  8. [Gl2] J. GLOBEVNIK, Perturbing analytic discs attached to maximal real submanifolds of ℂN, Indag. Math., N. S., 7 (1996), 37-46. Zbl0861.32013MR99b:32023
  9. [O] Y.-G. OH, Riemann-Hilbert problem and application to the perturbation theory of analytic discs, Kyungpook Math. J., 35 (1995), 39-75. Zbl0853.32017MR96j:32013
  10. [P1] J. PLEMELJ, Riemannsche Funktionenscharen mit gegebener Monodromiegruppe, Monatsh. Math. Phys., 19 (1908), 211-246. Zbl39.0461.01JFM39.0461.01
  11. [Po] Ch. POMMERENKE, Boundary behaviour of conformal maps, Grundl. der Math. Wiss., 299, Springer-Verlag, Berlin (1992). Zbl0762.30001MR95b:30008
  12. [PS] A. PRESSLEY and G. SEGAL, Loop groups., Oxford Science Publ., Clarendon Press, Oxford, 1986. Zbl0618.22011MR88i:22049
  13. [Ve1] N. P. VEKUA, Systems of singular integral equations, Nordhoff, Groningen, 1967. 
  14. [Ve2] N. P. VEKUA, Systems of singular integral equations. (2nd edition, Russian) Nauka, Moscow, 1970. 

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