Asymptotic behavior for H-holomorphic cylinders of small area
{\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 {\ma...
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| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
21 September 2019
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| In: |
Journal of fixed point theory and applications
Year: 2019, Jahrgang: 21, Heft: 4 |
| ISSN: | 1661-7746 |
| DOI: | 10.1007/s11784-019-0735-6 |
| Online-Zugang: | Verlag, Volltext: https://doi.org/10.1007/s11784-019-0735-6
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| Verfasserangaben: | Alexandru Doicu and Urs Fuchs |
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| 520 | |a {\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. | ||
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