Riemann maps in almost complex manifolds
Bernard Coupet; Hervé Gaussier; Alexandre Sukhov
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2003)
- Volume: 2, Issue: 4, page 761-785
- ISSN: 0391-173X
Access Full Article
topAbstract
topHow to cite
topCoupet, Bernard, Gaussier, Hervé, and Sukhov, Alexandre. "Riemann maps in almost complex manifolds." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 2.4 (2003): 761-785. <http://eudml.org/doc/84518>.
@article{Coupet2003,
abstract = {We prove the existence of stationary discs in the ball for small almost complex deformations of the standard structure. We define a local analogue of the Riemann map and establish its main properties. These constructions are applied to study the local geometry of almost complex manifolds and their morphisms.},
author = {Coupet, Bernard, Gaussier, Hervé, Sukhov, Alexandre},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {4},
pages = {761-785},
publisher = {Scuola normale superiore},
title = {Riemann maps in almost complex manifolds},
url = {http://eudml.org/doc/84518},
volume = {2},
year = {2003},
}
TY - JOUR
AU - Coupet, Bernard
AU - Gaussier, Hervé
AU - Sukhov, Alexandre
TI - Riemann maps in almost complex manifolds
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2003
PB - Scuola normale superiore
VL - 2
IS - 4
SP - 761
EP - 785
AB - We prove the existence of stationary discs in the ball for small almost complex deformations of the standard structure. We define a local analogue of the Riemann map and establish its main properties. These constructions are applied to study the local geometry of almost complex manifolds and their morphisms.
LA - eng
UR - http://eudml.org/doc/84518
ER -
References
top- [1] Z. Balogh – Ch. Leuenberger, Higher dimensional Riemann maps, Internat. J. Math. 9 (1998), 421-442. Zbl0916.32019MR1635177
- [2] D. Bennequin, Topologie symplectique, convexité holomorphe holomorphe et structures de contact [d’après Y. Eliashberg, D. Mc Duff et al.], Astérisque 189-190 (1990), 285-323. Zbl0755.32009MR1099880
- [3] J. Bland, Contact geometry and CR structures on , Acta Math. 172 (1994), 1-49. Zbl0814.32002MR1263996
- [4] J. Bland – T. Duchamp, Moduli for pointed convex domains, Invent. Math. 104 (1991), 61-112. Zbl0731.32010MR1094047
- [5] J. Bland – T. Duchamp – M. Kalka, A characterization of by its automorphism group, Lecture Notes in Math. 1268 (1987), 60-65. Zbl0621.32030MR907053
- [6] M. Cerne, Stationary discs of fibrations over the circle, Internat. J. Math. 6 (1995), 805-823. Zbl0841.32007MR1353996
- [7] E. Chirka, Regularity of boundaries of analytic sets, Math. USSR-Sb. 45 (1983), 291-336. Zbl0525.32005MR648411
- [8] K. Clancey – I. Gohberg, “Factorization of matrix functions and singular integral operators”, Birkhauser, Basel, Boston, Stuttgart, 1981. Zbl0474.47023MR657762
- [9] C. Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. math. 26 (1974), 1-65. Zbl0289.32012MR350069
- [10] J. Globevnik, Perturbation by analytic discs along maximal real submanifolds of , Math. Z. 217 (1994), 287-316. Zbl0806.58044MR1296398
- [11] J. Globevnik, Perturbing analytic discs attached to a maximal totally real submanifolds of , Indag. Math. 7 (1996), 37-46. Zbl0861.32013MR1621348
- [12] S. Ishihara – K. Yano, “Tangent and cotangent bundles: differential geometry”, Pure and Applied Mathematics, No. 16, Marcel Dekker Inc., New York, 1973. Zbl0262.53024MR350650
- [13] L. Lempert, La métrique de Kobayashi et la représentation des domaines sur la boule, Bull. Soc. Math. France 109 (1981), 427-474. Zbl0492.32025MR660145
- [14] L. Lempert, Solving the degenerate complex Monge-Ampère equation with one concentrated singularity, Math. Ann. 263 (1983), 515-532. Zbl0531.35020MR707246
- [15] L. Lempert, A precise result on the boundary regularity of biholomorphic mappings, Math. Z. 193 (1986), 559-579. Zbl0603.32013MR867348
- [16] L. Lempert, Holomorphic invariants, normal forms and moduli space of convex domains, Ann. of Math. 128 (1988), 47-78. Zbl0658.32015MR951507
- [17] L. Lempert, Erratum: A precise result on the boundary regularity of biholomorphic mappings, Math. Z. 206 (1991), 501-504. Zbl0716.32018MR1095768
- [18] P. Libermann, Problèmes d’équivalence relatifs à une structure presque complexe sur une variété à quatre dimensions, Acad. Roy. Belgique Bull. Cl. Sci. (5) 36 (1950), 742-755. Zbl0057.38204MR40791
- [19] M. Y. Pang, Smoothness of the Kobayashi metric of non-convex domains, Internat. J. Math. 4 (1993), 953-987. Zbl0795.32008MR1250257
- [20] S. Semmes, A generalization of Riemann mappings and geometric structures on a space of domains in , Mem. Amer. Math. Soc. 98 (1992), vi+98pp. Zbl0777.32015MR1113614
- [21] J. C. Sikorav, “Some properties of holomorphic curves in almost complex manifolds”, pp.165-189, In: “Holomorphic curves in symplectic geometry", Michèle Audin, Jacques Lafontaine Editors, Birkhäuser, 1994. MR1274929
- [22] A. Spiro – S. Trapani, Eversive maps of bounded convex domains in , J. Geom. Anal. 12 (2002), 695-715. Zbl1039.32019MR1916865
- [23] A. Tumanov, Extremal discs and the regularity of CR mappings in higher codimension, Amer. J. Math. 123 (2001), 445-473. Zbl0995.32024MR1833148
- [24] N. P. Vekua, “Systems of singular integral equations”, Nordholf, Groningen, 1967. Zbl0166.09802MR211220
- [25] S. Webster, On the reflection principle in several complex variables, Proc. Amer. Math. Soc. 71 (1978), 26-28. Zbl0626.32019MR477138
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.