A zoll counterexample to a geodesic length conjecture
Balacheff, Florent Nicolas (University of Geneva. Department of Mathematics)
Croke, Christopher (University of Pennsylvania. Department of Mathematics)
Katz, Mikhail G. (Bar Ilan University. Department of Mathematics)

Date:	2009
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.
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Closed geodesic ; Diameter ; Guillemin deformation ; Sphere ; Systole ; Zoll surface
Published in:	Geometric and Functional Analysis, Vol. 19, Issue 1 (May 2009) , p. 1-10, ISSN 1420-8970

DOI: 10.1007/s00039-009-0708-9

Postprint 11 p, 439.3 KB

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