2026-04-17T05:18:01Zhttps://recercat.cat/oai/request

oai:recercat.cat:2072/4729182025-04-03T10:13:10Zcom_2072_98col_2072_378192

00925njm 22002777a 4500 dc Balacheff, Florent Nicolas author Croke, Christopher author Katz, Mikhail G. author 2009 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. Closed geodesic Diameter Guillemin deformation Sphere Systole Zoll surface A zoll counterexample to a geodesic length conjecture