Scientific article
English

A Zoll Counterexample to a Geodesic Length Conjecture

Published inGeometric and functional analysis, vol. 19, no. 1, p. 1-10
Publication date2009
Abstract

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.

Citation (ISO format)
BALACHEFF, Florent Nicolas, CROKE, Christopher, KATZ, Mikhail G. A Zoll Counterexample to a Geodesic Length Conjecture. In: Geometric and functional analysis, 2009, vol. 19, n° 1, p. 1–10. doi: 10.1007/s00039-009-0708-9
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accessLevelRestricted
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Journal ISSN1016-443X
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