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Stationary discs glued to a Levi non-degenerate hypersurface
Author(s):
Léa
Blanc-Centi
Journal:
Trans. Amer. Math. Soc.
361
(2009),
3223-3239.
MSC (2000):
Primary 32A10, 32V40
Posted:
December 31, 2008
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Abstract:
We obtain an explicit parametrization of stationary discs glued to some Levi non-degenerate hypersurfaces. These discs form a family which is invariant under the action of biholomorphisms. We use this parametrization to construct a local circular representation of these hypersurfaces. As a corollary, we get the uniqueness of biholomorphisms with given 1-jet at some convenient point.
References:
-
- 1.
- G. D. BIRKHOFF, A theorem on matrices of analytic functions, Math. Ann. 74 (1913) no. 1, 122-133. MR 1511753
- 2.
- M. ČERNE, Regularity of discs attached to a submanifold of
 , Journal d'analyse mathématique 72 (1997). MR 1482997 (99c:32025) - 3.
- S. S. CHERN, J. K. MOSER, Real hypersurfaces in complex manifolds, Acta Mathematica 133 (1975). MR 0425155 (54:13112)
- 4.
- E. M. CHIRKA, Regularity of the boundaries of analytic sets, Mat. Sb. 45 (1983), 291-336. MR 648411 (83f:32009)
- 5.
- K. CLANCEY, I. GOHBERG, Factorization of matrix functions and singular integral operators, Birkhäuser Verlag, 1981. MR 657762 (84a:47016)
- 6.
- B. COUPET, H. GAUSSIER, A. SUKHOV, Riemann maps in almost complex manifolds, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 2 (2003), no. 4, 761-785. MR 2040642 (2006a:32030)
- 7.
- J. GLOBEVNIK, Perturbation by analytic discs along maximal real submanifolds of
 , Math. Z. 217 (1994), 287-316. MR 1296398 (95j:32031) - 8.
- L. LEMPERT, La métrique de Kobayashi et la représentation des domaines sur la boule, Bull. Math. Soc. France 109 (1981), 427-474. MR 660145 (84d:32036)
- 9.
- Y.-G. OH, Riemann-Hilbert problem and application to the perturbation theory of analytic discs, Kyungpook Math. J. 35 (1995) no. 1, 39-75. MR 1345070 (96j:32013)
- 10.
- H. POINCARé, Les fonctions analytiques de deux variables et la représentation conforme, Rend. Circ. Mat. Palermo 23 (1907), 185-220.
- 11.
- A. SUKHOV, A. TUMANOV. Stationary discs and geometry of CR manifolds of codimension two, Internat. J. Math. 12 (2001), no. 8, 877-890. MR 1863284 (2002i:32030)
- 12.
- A. TUMANOV, Extremal discs and the regularity of CR mappings in higher codimension, Amer. J. Math. 123 (2001) no.3, 445-473. MR 1833148 (2002f:32063)
- 13.
- I. N. VEKUA, Generalized analytic functions, Addison-Wesley Publishing Company, International series of monographs in pure and applied mathematics (1962). MR 0108572 (21:7288)
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Additional Information:
Léa
Blanc-Centi
Affiliation:
L.A.T.P., C.M.I., Universites de Marseille, 39 rue Joliot-Curie, 13453 Marseille Cedex 13, France
Address at time of publication:
U.M.P.A., E.N.S. Lyon, 46 allée d'Italie, 69364 Lyon Cedex 07, France
Email:
lea@cmi.univ-mrs.fr, lea.blanc-centi@umpa.ens-lyon.fr
DOI:
10.1090/S0002-9947-08-04737-5
PII:
S 0002-9947(08)04737-5
Keywords:
Analytic discs,
Riemann maps
Received by editor(s):
February 8, 2007
Received by editor(s) in revised form:
July 23, 2007
Posted:
December 31, 2008
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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