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A zoll counterexample to a geodesic length conjecture Balacheff, Florent Nicolas Croke, Christopher Katz, Mikhail G. Closed geodesic Diameter Guillemin deformation Sphere Systole Zoll surface We construct a counterexample to a conjectured inequality L ≤ 2D, relating the diameter D and the least length L of a nontrivial closed geodesic, for a Riemannian metric on the 2-sphere. The construction relies on Guillemin's theorem concerning the existence of Zoll surfaces integrating an arbitrary infinitesimal odd deformation of the round metric. Thus the round metric is not optimal for the ratio L/D. 2009 Article https://ddd.uab.cat/record/287723 urn:10.1007/s00039-009-0708-9 urn:oai:ddd.uab.cat:287723 urn:pure_id:153316310 urn:scopus_id:59649109269 urn:oai:egreta.uab.cat:publications/d0859d7b-d083-4be5-81e7-042492d94cbf eng Geometric and Functional Analysis ; Vol. 19, Issue 1 (May 2009), p. 1-10 open access Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets. https://rightsstatements.org/vocab/InC/1.0/ application/pdf