Filling by holomorphic curves in symplectic 4-manifolds

Transactions of the American Mathematical Society

Volumn 350, Issue 1, 1998, Pages 213-250

  Rugang, Y E ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

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EID: 21944434403     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (25)

1. [A] M. Audin, Symplectic and almost complex manifolds, in Holomorphic Curves in Symlectic Geometry, by M. Audin and J. Lafontaine (editors), Birkhäuser, 1994, pp. 41-74. MR 951:58005
2. [AA] F. J. Almgren and W. K. Allard, On the radial behavior of minimal surfaces and the uniqueness of their tangent cones, Ann. Math. 113 (1981), 215-265. MR 83k:49069
3. [B] E. Bishop, Differentiate manifolds in complex Euclidean space, Duke Math. J. 32 (1965), 1-22. MR 34:369
4. [BG] E. Bedford and B. Gaveau, Envelopes of holomorphy of certain 2-spheres in ℂ2, Amer. J. Math. 105 (1983), 975-1009. MR 84k:32016
5. 2, J. Amer. Math. Soc. 4 (1991), 623-646. MR 92j:32034
6. [El] Y. Eliashberg, Filling by holomorphic disks and its applications, Geometry of Lowdimensional Manifolds, 2 (Durham, 1989), London Math. Soc. Lecture Note Ser., vol. 151, Cambridge Univ. Press, 1990, pp. 45-67. MR 93g:53060
7. [E2] Y. Eliashberg, Topology of 2-knots in R4 and symplectic geometry, The Floer Memorial Volume, Progr. Math., vol. 133, Birkhäuser,.Basel, 1995, pp. 335-353. MR 9Gj:57023
8. [F] A. Floer, The unregularized gradient flow of the symplectic action, Comm. Pure Appl. Math. 41 (1988), 775-813. MR 89g:58065
9. [G] M. Gromov, Pseudo-holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307-347. MR 87j:53053
10. [H] H. Hofer, Pseudo holomorphic spheres in symplectizations with applications to the Weinstein conjecture in dimension three, Invent. Math. 114 (1993), 515-563. MR 94j:58064
11. [Ml] D. McDuff, The local behavior of holomorphic curves in almost complex 4-manifolds, J. Diff. Geom. 34 (1981), 143-164. MR 93e:53050
12. [M2] D. McDuff, Singularities of J-holomorphic curves in almost complex 4-manifolds, J. Geom. Anal. 2 (1992), 249-266. MR 93g:58032
13. [M3] D. McDuff, The structure of rational and ruled symplectic 4-manijolds, J. Amer. Math. Soc. 3 (1990), 679-712; erratum, 5 (1992), 987-988. MR 91k:58042; MR 93k:58098
14. [M4] D. McDuff, Examples of symplectic structures, Invent. Math. 89 (1987), 13-36. MR 88m:58061
15. [M5] D. McDuff, Singularities and positivity of intersections of J-holomorphic curves in symplectic 4-manifolds, in Holomorphic Curves in Symplectic Geometry, edited by M. Audin and J. Lafontaine (editors), Birkhäuser, 1994, pp. 191-215. MR 951:58005
16. [MS] D. McDuff and D. Salamon, Symplectic Geometry, Lecture Notes, Cambridge, 1993.
17. [MT] D. McDuff and L. Traynor, Cambridge Univ. Press, 1993, pp. 169-182 in Symplectic Geometry. MR 95j:58052
18. [MW] M. J. Micallef and B. White, The structure of branch points in area minimizing surfaces and in pseudoholomorphic curves, preprint. Ann. Math. 141 (1995), 35-85. MR 96a:58063
19. [SU] J. Sacks and K. Uhlenbeck, The existence of minimal immersions of 2-spheres, Ann. Math. (2) 113 (1981), 1-24. MR 82f:58035
20. [SI] L. Simon, Asymptotics for a class of non-linear evolution equations, with applications to geometric problems, Ann. Math. (2) 118 (1983), 525-572. MR 85b:58121
21. [S2] L. Simon, Cylindrical tangent cones and the singular set of minimal submanifolds, J. Diff. Geom. 38 (1993), 585-652. MR 95a:58026
22. [S3] L. Simon, On the singularities of harmonic maps, preprint.
23. [V] I. N. Vekua, Generalized analytic functions, Pergamon Press, Oxford, and Addison-Wesley, Reading, MA, 1962. MR 27:321
24. [Yl] R. Ye, Gromov's compactness theorem for pseudo holomorphic curves, Trans. Amer. Math. Soc. 342 (1994), 671-694. MR 94f:58030
25. [Y2] R. Ye, Filling by holomorphic disks in symplectic , 4-mam/oWs, preprint, Centre de Mathrhatiques et de Leurs Applications, ENS Cachan, 1994.