Asymptotic behavior for H-holomorphic cylinders of small area

• Verfasst von: Doicu, Alexandru [VerfasserIn]
• Verfasst von: Fuchs, Urs [VerfasserIn]
• Titel: Asymptotic behavior for H-holomorphic cylinders of small area
• Verf.angabe: Alexandru Doicu and Urs Fuchs
• E-Jahr: 2019
• Jahr: 21 September 2019
• Umfang: 51 S.
• Teil: volume:21
• Teil: year:2019
• Teil: number:4
• Teil: extent:51
• Fussnoten: Gesehen am 15.10.2019
• Titel Quelle: Enthalten in: Journal of fixed point theory and applications
• Ort Quelle: Cham (ZG) : Springer International Publishing AG, 2007
• Jahr Quelle: 2019
• Band/Heft Quelle: 21(2019,4) Artikel-Nummer 96, 51 Seiten
• ISSN Quelle: 1661-7746
• DOI: doi:10.1007/s11784-019-0735-6
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: 32Q65
• Sach-SW: 53D35
• Sach-SW: 53D42
• K10plus-PPN: 1678906433

Abstract

{\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 d\alpha \alpha -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.