A Zoll counterexample to a geodesic length conjecture

Details A Zoll counterexample to a geodesic length conjecture A Zoll counterexample to a geodesic length conjecture

2007-11-08

arxiv.org/abs/0711.1229v2

Mathematics

Differential Geometry

10 pages; to appear in Geometric and Functional Analysis

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

A Zoll counterexample to a geodesic length conjecture does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Zoll counterexample to a geodesic length conjecture, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Zoll counterexample to a geodesic length conjecture will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-377478