Symplectic field theory is the study of J-holomorphic curves in almost complex manifolds with cylindrical ends. One natural generalization is to replace "cylindrical" by "asymptotically cylindrical". We generalize a number of asymptotic results about the behavior of J-holomorphic curves near infinity to the asymptotically cylindrical setting. We also sketch how these asymptotic results allow compactness theorems in symplectic field theory to be extended to the asymptotically cylindrical case.
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© 2015 Mathematical Sciences.
- Asymptotically cylindrical almost complex structure
- Hofer energy
- J-holomorphic curve
- Stable Hamiltonian structure
- Symplectic field theory