TY - JOUR
T1 - Asymptotic behavior for H -holomorphic cylinders of small area
AU - Doicu, Alexandru
AU - Fuchs, Urs
PY - 2019/12/1
Y1 - 2019/12/1
N2 - 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 H-holomorphic cylinders with small dα-energies. Our results can be seen as a first step toward establishing the compactness of the moduli space of 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.
AB - 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 H-holomorphic cylinders with small dα-energies. Our results can be seen as a first step toward establishing the compactness of the moduli space of 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.
UR - http://www.scopus.com/inward/record.url?scp=85073218934&partnerID=8YFLogxK
U2 - 10.1007/s11784-019-0735-6
DO - 10.1007/s11784-019-0735-6
M3 - Article
AN - SCOPUS:85073218934
SN - 1661-7738
VL - 21
JO - Journal of Fixed Point Theory and Applications
JF - Journal of Fixed Point Theory and Applications
IS - 4
M1 - 96
ER -