| In this talk we discuss the construction of Zoll surfaces
(surfaces all of whose geodesics are closed of length 2\pi) and how
they can be used to find interesting examples.
In particular we (discussing a joint work with Balacheff and Katz)
construct Riemannian metrics on the 2-sphere with L>2D relating the
diameter D and the least length L of a nontrivial
closed geodesic. This gives a counterexample to a conjecture of
Nabutovsky and Rotman. The construction relies on Guillemin's theorem
concerning the existence of
Zoll surfaces integrating an arbitrary infinitesimal odd deformation of
the round metric. We conclude that the round metric is not even locally
optimal for the ratio L/D. |
