Asymptotic behavior for H-holomorphic cylinders of small area - Doicu, Alexandru; Fuchs, Urs (Journal of fixed point theory and applications, 2019)
{\mathcal {H}}{\mathcal {H}}-holomorphic curves are solutions of a modified pseudoholomorphic curve equation involving a harmonic 1-form as perturbation term. Following Hofer et al. (Dyn Syst Ergod Theory 22(5):1451-1486, 2002), we establish an asymptotic behavior of a sequence of finite energy {\mathcal {H}}{\mathcal {H}}-holomorphic cylinders with small dα α -energies. Our results can be seen as a first step toward establishing the compactness of the moduli space of {\mathcal {H}}{\mathcal {H}}-holomorphic curves, which in turn, due to the program initiated in Abbas et al. (Comment Math Helv 80:771-793, 2005), can be used for proving the generalized Weinstein conjecture.