PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

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Title:Zoll surfaces as counterexamples to a geodesic length conjecture
Seminar:Center for Dynamics and Geometry Seminars
Speaker:Chris Croke (U Penn)
Abstract:
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.

Room Reservation Information

Room Number:MB106
Date:10 / 10 / 2007
Time:03:35pm - 04:35pm