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Filling by holomorphic curves in symplectic 4-manifolds

Author(s): Rugang Ye
Journal: Trans. Amer. Math. Soc. 350 (1998), 213-250.
MSC (1991): Primary 53C15; Secondary 32C25
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Abstract: We develop a general framework for embedded (immersed) $J$-holomorphic curves and a systematic treatment of the theory of filling by holomorphic curves in 4-dimensional symplectic manifolds. In particular, a deformation theory and an intersection theory for $J$-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 $J$-holomorphic spheres, culminating in the construction of singular fillings.

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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: 10.1090/S0002-9947-98-01970-9
PII: S 0002-9947(98)01970-9
Received by editor(s): January 24, 1996
Additional Notes: Partially supported by NSF
Copyright of article: Copyright 1998, American Mathematical Society

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