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.Comment: 10 pages; to appear in Geometric and Functional Analysi
