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Symplectic Field Theory studies J-holomorphic curves in almost complexmanifolds with cylindrical ends. One natural generalization is to replace'cylindrical' by 'asymptotically cylindrical'. In this article, we generalizethe asymptotic results about the behavior of J-holomorphic curves near infinityto the asymptotically cylindrical setting. We also sketch how these asymptoticresults allow the main compactness theorems in Symplectic Field Theory provedby Bourgeois, Eliashberg, Hofer, Wysocki and Zehnder to be extended to theasymptotically cylindrical case.

On J-holomorphic curves in almost complex manifolds with asymptotically cylindrical ends