Filling by holomorphic curves in symplectic 4manifolds
Author:
Rugang Ye
Journal:
Trans. Amer. Math. Soc. 350 (1998), 213250
MSC (1991):
Primary 53C15; Secondary 32C25
MathSciNet review:
1422913
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Abstract: We develop a general framework for embedded (immersed) holomorphic curves and a systematic treatment of the theory of filling by holomorphic curves in 4dimensional symplectic manifolds. In particular, a deformation theory and an intersection theory for holomorphic curves with boundary are developed. Bishop's local filling theorem is extended to almost complex manifolds. Existence and uniqueness of global fillings are given complete proofs. Then they are extended to the situation with nontrivial holomorphic spheres, culminating in the construction of singular fillings.
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 H. Hofer, Pseudo holomorphic spheres in symplectizations with applications to the Weinstein conjecture in dimension three, Invent. Math. 114 (1993), 515563. MR 94j:58064
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 D. McDuff, The local behavior of holomorphic curves in almost complex 4manifolds, J. Diff. Geom. 34 (1981), 143164. MR 93e:53050
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 D. McDuff, Singularities of Jholomorphic curves in almost complex 4manifolds, J. Geom. Anal. 2 (1992), 249266. MR 93g:58032
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 [MS]
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 J. Sacks and K. Uhlenbeck, The existence of minimal immersions of 2spheres, Ann. Math. (2) 113 (1981), 124. MR 82f:58035
 [S1]
 L. Simon, Asymptotics for a class of nonlinear evolution equations, with applications to geometric problems, Ann. Math. (2) 118 (1983), 525572. MR 85b:58121
 [S2]
 L. Simon, Cylindrical tangent cones and the singular set of minimal submanifolds, J. Diff. Geom. 38 (1993), 585652. MR 95a:58026
 [S3]
 L. Simon, On the singularities of harmonic maps, preprint.
 [V]
 I. N. Vekua, Generalized analytic functions, Pergamon Press, Oxford, and AddisonWesley, Reading, MA, 1962. MR 27:321
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Additional Information
Rugang Ye
Affiliation:
Department of Mathematics, University of California, Santa Barbara, California 93106
Email:
yer@math.ucsb.edu
DOI:
http://dx.doi.org/10.1090/S0002994798019709
PII:
S 00029947(98)019709
Received by editor(s):
January 24, 1996
Additional Notes:
Partially supported by NSF
Article copyright:
© Copyright 1998
American Mathematical Society
