We give a necessary condition for the existence of extremal pseudoholomorphic discs on some domains in where is a small almost complex deformation of the standard complex structure.
@article{ASNSP_2010_5_9_4_759_0,
author = {Gaussier, Herv\'e and Joo, Jae-Cheon},
title = {Extremal discs in almost complex spaces},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {759--783},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 9},
number = {4},
year = {2010},
mrnumber = {2789474},
zbl = {1209.32003},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2010_5_9_4_759_0/}
}
TY - JOUR AU - Gaussier, Hervé AU - Joo, Jae-Cheon TI - Extremal discs in almost complex spaces JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2010 SP - 759 EP - 783 VL - 9 IS - 4 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2010_5_9_4_759_0/ LA - en ID - ASNSP_2010_5_9_4_759_0 ER -
%0 Journal Article %A Gaussier, Hervé %A Joo, Jae-Cheon %T Extremal discs in almost complex spaces %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2010 %P 759-783 %V 9 %N 4 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2010_5_9_4_759_0/ %G en %F ASNSP_2010_5_9_4_759_0
Gaussier, Hervé; Joo, Jae-Cheon. Extremal discs in almost complex spaces. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 4, pp. 759-783. http://www.numdam.org/item/ASNSP_2010_5_9_4_759_0/
[1] , A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order, J. Math. Pures Appl. (9) 36 (1957), 235–249. | MR | Zbl
[2] and , “Holomorphic Curves in Symplectic Geometry”, Progr. Math., Vol. 117, Birkhäuser, Basel, 1994. | MR | Zbl
[3] and , Moduli for pointed convex domains, Invent. Math. 104 (1991), 61–112. | EuDML | MR | Zbl
[4] and , Rigidity of holomorphic mappings and a new Schwarz lemma at the boundary, J. Amer. Math. Soc. 7 (1994), 661–676. | MR | Zbl
[5] , The Kobayashi geometry of Lee’s model of dimension 6, preprint.
[6] , and , Fefferman’s mapping theorem on almost complex manifolds in complex dimension two, Math. Z. 250 (2005), 59–90. | MR | Zbl
[7] , and , Riemann maps in almost complex manifolds, Ann. Scuola Norm. Super. Pisa Cl. Sci. (5) 2 (2003), 761–785. | EuDML | Numdam | MR | Zbl
[8] and , On the geometry of model almost complex manifolds with boundary, Math. Z. 254 (2006), 567–589. | MR | Zbl
[9] , Pseudo holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307–347. | EuDML | MR | Zbl
[10] and , On the local behavior of solutions of non-parabolic partial differential equations, Amer. J. Math. 75 (1953), 449–476. | MR | Zbl
[11] and , “Tangent and Cotangent Bundles: Differential Geometry”, Pure and Applied Mathematics, No. 16, Marcel Dekker, Inc., New York, 1973. | MR | Zbl
[12] and , Boundary Values and Boundary Uniqueness of -Holomorphic Mappings, arXiv:0902.4800. | MR | Zbl
[13] , Strongly pseudoconvex homogeneous domains in almost complex manifolds, J. Reine Angew. Math. 623 (2008), 123–160. | MR | Zbl
[14] , La métrique de Kobayashi et la représentation des domaines sur la boule, (French) [The Kobayashi metric and the representation of domains on the ball] Bull. Soc. Math. France 109 (1981), 427–474. | EuDML | Numdam | MR | Zbl
[15] , A precise result on the boundary regularity of biholomorphic mappings, Math. Z. 193 (1986), 559–579. | EuDML | MR | Zbl
[16] , Holomorphic invariants, normal forms, and the moduli space of convex domains, Ann. of Math. 128 (1988), 43–78. | MR | Zbl
[17] and , The tangent bundle of an almost complex manifold, Canad. Math. Bull. 44 (2001), 70–79. | MR | Zbl
[18] and , “-holomorphic Curves and Symplectic Topology”, Amer. Math. Soc., Coll. Publ., Vol. 52, 2004. | MR | Zbl
[19] M. -Y. Pang, Smoothness of the Kobayashi metric of nonconvex domains, Internat. J. Math. 4 (1993), 953–987. | MR | Zbl
[20] , Real and complex Monge Ampère equations and the geometry of strictly convex domains, Publ. Res. Inst. Math. Sci. 20 (1984), 867–875. | MR | Zbl
[21] , The Euler Lagrange equations for extremal holomorphic mappings of the unit disk, Michigan Math. J. 30 (1983), 317–333. | MR
[22] , Total reality of conormal bundles of hypersurfaces in almost complex manifolds, Int. J. Geom. Methods Mod. Phys. 3 (2006), 1255–1262. | MR | Zbl
[23] and , An existence theorem for stationary discs in almost complex manifolds, J. Math. Anal. Appl. 327 (2007), 269–286. | MR | Zbl
[24] , Extremal discs and the regularity of CR mappings in higher codimension, Amer. J. Math. 123 (2001), 445–473. | MR | Zbl
[25] , “Generalized Analytic Functions”, Pergamon Press, London-Paris-Frankfurt; Addison-Wesley Publishing Co., Inc., Reading, Mass. 1962. | MR
