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

TL;DR

This paper extends the understanding of J-holomorphic curves in almost complex manifolds from cylindrical to asymptotically cylindrical ends, broadening the scope of Symplectic Field Theory's compactness results.

Contribution

It generalizes asymptotic behavior results of J-holomorphic curves to asymptotically cylindrical settings, enabling extension of key compactness theorems.

Findings

Generalized asymptotic results for J-holomorphic curves

Extended compactness theorems to asymptotically cylindrical cases

Provided a framework for analyzing curves in more general geometries

Abstract

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