Gromov Compactness Theorem for J-Complex Curves with Boundary

International Mathematics Research Notices

Volumn 2000, Issue 22, 2000, Pages 1167-1206

  Ivashkovich, S ^a,b   Shevchishin, V ^a,c  

^a INSTITUTE OF HYDROBIOLOGY   (Ukraine)

^b UNIV LILLE   (France)

^c RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038594448     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: 10.1155/s1073792800000581     Document Type: Article

References (19)

1. [Ab] W. Abikoff, The Real Analytic Theory of Teichmüller Space, Lecture Notes in Math. 80, Springer, Berlin, 1980.
2. [DM] P. Deligne and D. Mumford, The irreducibility of the space of curves of given genus, Inst. Hautes Études Sci. Publ. Math. 36 (1969), 75-109.
3. [Du] J. Dufresnoy, Sur les domaines couverts par les valeurs d'une fonction méromorphe ou algébroïde, Ann. Sci. École Norm. Sup. (3), 58 (1941), 179-259.
4. [FO] K. Fukaya and K. Ono, Arnold conjecture and Gromov-Witten invariant, Topology 38 (1999), 933-1048.
5. [G] M. Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307-347.
6. [Hum] C. Hummel, Gromov's Compactness Theorem for Pseudo-Holomorphic Curves, Progr. Math. 151, Birkhäuser, Basel, 1997.
7. [IS1] S. Ivashkovich and S. Shevchishin, Structure of the moduli space in a neighborhood of a cusp-curve and meromorphic hulls, Invent. Math. 136 (1999), 571-602.
8. [IS2] _, Gromov compactness theorem for stable curves, http://www.arXiv.org/abs/math.DG/9903047.
9. [K] M. Kontsevich, "Enumeration of rational curves via torus actions" in The Moduli Spaces of Curves (Texel Island, Netherlands, 1994), Prog. Math. 129 Birkhäuser, Boston, 1995, 335-368.
10. [KM] M. Kontsevich and Yu. Manin, Gromov-Witten classes, quantum cohomology, and enumerative geometry, Comm. Math. Phys. 164 (1994), 525-562.
11. [Lh] O. Lehto, The spherical derivative of meromorphic functions in the neighbourhood of an isolated singularity, Comment Math. Helv. 33 (1959), 196-205.
12. [McDS] D. McDuff and D. Salamon, J-holomorphic Curves and Quantum Cohomology, Univ. Lecture Ser. 6, Amer. Math. Soc., Providence, 1994.
13. [MiR] I. Mundet i Riera, Hamiltonian Gromov-Witten Invariants, http://www.arXiv.org/abs/math.SG/0002121.
14. [Pa] T. H. Parker, Bubble tree convergence for harmonic maps, J. Differential Geom. 44 (1996), 595-633.
15. [PW] T. H. Parker and J. G. Wolfson, Pseudo-holomorphic maps and bubble trees, J. Geom. Anal. 3 (1993), 63-98.
16. [SU] J. Sacks and K. Uhlenbeck, The existence of minimal immersions of 2-spheres, Ann. of Math. (2) 113 (1981), 1-24.
17. [S] J.-C. Sikorav, "Some properties of holomorphic curves in almost complex manifolds" in Holomorphic Curves in Symplectic Geometry, Progr. Math. 117, Birkhäuser, Basel, 1994, 165-189.
18. [Wo] J. G. Wolfson, Gromov's compactness of pseudo-holomorphic curves and symplectic geome- try, J. Differential Geom. 28 (1988), 383-405.
19. [Ye] R. Ye, Gromov's compactness theorem for pseudo holomorphic curves, Trans. Amer. Math. Soc. 342 (1994), 671-694.