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Title: Dynamically convex Finsler metrics and J-holomorphic embedding of asymptotic cylinders
Contributor(s): Harris, Adam  (author)orcid ; Paternain, Gabriel P (author)
Publication Date: 2008
DOI: 10.1007/s10455-008-9111-2
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Abstract: We explore the relationship between contact forms on S³ defined by Finsler metrics on S² and the theory developed by H. Hofer, K.Wysocki and E. Zehnder (Hofer et al. Ann. Math. 148, 197–289, 1998; Ann. Math. 157, 125–255, 2003). We show that a Finsler metric on S² with curvature K ≥ 1 and with all geodesic loops of length >π is dynamically convex and hence it has either two or infinitely many closed geodesics. We also explain how to explicitly construct J -holomorphic embeddings of cylinders asymptotic to Reeb orbits of contact structures arising from Finsler metrics on S² with K = 1, thus complementing the results obtained in Harris and Wysocki (Trans. Am. Math. Soc., to appear).
Publication Type: Journal Article
Source of Publication: Annals of Global Analysis and Geometry, 34(2), p. 115-134
Publisher: Springer Netherlands
Place of Publication: Amsterdam, The Netherlands
ISSN: 0232-704X
Field of Research (FOR): 010111 Real and Complex Functions (incl Several Variables)
Socio-Economic Outcome Codes: 970101 Expanding Knowledge in the Mathematical Sciences
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
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