Filling by holomorphic curves in

symplectic 4-manifolds

Author:
Rugang Ye

Journal:
Trans. Amer. Math. Soc. **350** (1998), 213-250

MSC (1991):
Primary 53C15; Secondary 32C25

DOI:
https://doi.org/10.1090/S0002-9947-98-01970-9

MathSciNet review:
1422913

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Abstract | References | Similar Articles | Additional Information

Abstract: We develop a general framework for embedded (immersed) -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 -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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Additional Information

**Rugang Ye**

Affiliation:
Department of Mathematics, University of California, Santa Barbara, California 93106

Email:
yer@math.ucsb.edu

DOI:
https://doi.org/10.1090/S0002-9947-98-01970-9

Received by editor(s):
January 24, 1996

Additional Notes:
Partially supported by NSF

Article copyright:
© Copyright 1998
American Mathematical Society