no. 5
Partial indices of analytic discs attached to lagrangian submanifolds of ℂ N
Annales de l'Institut Fourier, Tome 46 (1996) no. 5, pp. 1307-1326.

Les entiers κ 1 ,...,κ N sont les indices partiels d’un disque analytique attaché à une sous-variété maximalement réelle de ℂ N si et seulement si κ j ≥2 pour au moins un j. Dans ce cas, il existe une sous-variété lagrangienne M de ℂ N et un disque analytique attaché à M avec indices partiels κ 1 ,...,κ N .

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 .

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     title = {Partial indices of analytic discs attached to lagrangian submanifolds of ${\mathbb {C}}^N$},
     journal = {Annales de l'Institut Fourier},
     pages = {1307--1326},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {46},
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     year = {1996},
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Globevnik, Josip. Partial indices of analytic discs attached to lagrangian submanifolds of ${\mathbb {C}}^N$. Annales de l'Institut Fourier, Tome 46 (1996) no. 5, pp. 1307-1326. doi : 10.5802/aif.1550. https://aif.centre-mersenne.org/articles/10.5802/aif.1550/

[Ch] E. M. Chirka, Regularity of boundaries of analytic sets. (Russian) Mat. Sb. (N. S.), 117 (159) (1982), 291-336, English translation in Math. USSR Sb., 45 (1983), 291-335. | MR | Zbl

[Č1] M. Černe, Minimal discs with free boundaries in a Lagrangian submanifold of ℂn, Indiana Univ. Math. J., 44 (1995), 153-164. | MR | Zbl

[Č2] M. Černe, Stationary discs of fibrations over the circle, Internat. J. Math., 6 (1995), 805-823. | MR | Zbl

[Č3] M. Černe, Analytic discs attached to a generating CR-manifold, Arkiv för Mat., 33 (1995), 217-248. | MR | Zbl

[Č4] M. Černe, Regularity of discs attached to a submanifold of ℂN, preprint | Zbl

[Fo] F. Forstnerič, Analytic discs with boundaries in a maximal real submanifold of C2, Ann. Inst. Fourier, 37-1 (1987), 1-44. | EuDML | Numdam | MR | Zbl

[Gl1] J. Globevnik, Perturbation by analytic discs along maximal real submanifolds of CN, Math. Z., 217 (1994), 287-316. | EuDML | MR | Zbl

[Gl2] J. Globevnik, Perturbing analytic discs attached to maximal real submanifolds of ℂN, Indag. Math., N. S., 7 (1996), 37-46. | MR | Zbl

[O] Y.-G. Oh, Riemann-Hilbert problem and application to the perturbation theory of analytic discs, Kyungpook Math. J., 35 (1995), 39-75. | MR | Zbl

[P1] J. Plemelj, Riemannsche Funktionenscharen mit gegebener Monodromiegruppe, Monatsh. Math. Phys., 19 (1908), 211-246. | JFM

[Po] Ch. Pommerenke, Boundary behaviour of conformal maps, Grundl. der Math. Wiss., 299, Springer-Verlag, Berlin (1992). | MR | Zbl

[PS] A. Pressley and G. Segal, Loop groups., Oxford Science Publ., Clarendon Press, Oxford, 1986. | MR | Zbl

[Ve1] N. P. Vekua, Systems of singular integral equations, Nordhoff, Groningen, 1967.

[Ve2] N. P. Vekua, Systems of singular integral equations. (2nd edition, Russian) Nauka, Moscow, 1970.

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