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https://hdl.handle.net/1959.11/2919
Title: | Dynamically convex Finsler metrics and J-holomorphic embedding of asymptotic cylinders | Contributor(s): | Harris, Adam (author) ; Paternain, Gabriel P (author) | Publication Date: | 2008 | DOI: | 10.1007/s10455-008-9111-2 | Handle Link: | https://hdl.handle.net/1959.11/2919 | 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: | Netherlands | ISSN: | 1572-9060 0232-704X |
Fields of Research (FoR) 2008: | 010111 Real and Complex Functions (incl Several Variables) | Socio-Economic Objective (SEO) 2008: | 970101 Expanding Knowledge in the Mathematical Sciences | Peer Reviewed: | Yes | HERDC Category Description: | C1 Refereed Article in a Scholarly Journal |
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Appears in Collections: | Journal Article |
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