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Depósito Digital de Documentos de la UAB Encontrados 3 registros  La búsqueda tardó 0.01 segundos. 
1.
11 p, 439.3 KB 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)
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. [...]
2009 - 10.1007/s00039-009-0708-9
Geometric and Functional Analysis, Vol. 19, Issue 1 (May 2009) , p. 1-10  
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2.
22 p, 506.0 KB Contact geometry and isosystolic inequalities / Alvarez Paiva, Juan Carlos (Université de Lille. Laboratoire Paul Painlevé) ; Balacheff, Florent Nicolas (Université de Lille. Laboratoire Paul Painlevé)
A long-standing open problem asks whether a Riemannian metric on the real projective space with the same volume as the canonical metric carries a periodic geodesic whose length is at most π. A contact-geometric reformulation of systolic geometry and the use of canonical perturbation theory allow us to solve a parametric version of this problem: if g s is a smooth, constant-volume deformation of the canonical metric that is not formally trivial, the length of the shortest periodic geodesic of the metric g s attains π as a strict local maximum at s = 0. [...]
2014 - 10.1007/s00039-014-0250-2
Geometric and Functional Analysis, Vol. 24, Issue 2 (April 2014) , p. 648-669  
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3.
32 p, 569.4 KB Short Loop Decompositions of Surfaces and the Geometry of Jacobians / Balacheff, Florent Nicolas (Université de Lille. Laboratoire Paul Painlevé) ; Parlier, Hugo (University of Fribourg. Department of Mathematics) ; Sabourau, Stéphane (Université Paris-Est Créteil. Laboratoire d'Analyse et de Mathématiques, Appliquées)
Given a Riemannian surface, we consider a naturally embedded graph which captures part of the topology and geometry of the surface. By studying this graph, we obtain results in three different directions. [...]
2012 - 10.1007/s00039-012-0147-x
Geometric and Functional Analysis, Vol. 22, Issue 1 (February 2012) , p. 37-73  
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