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Results overview: Found 6 records in 0.02 seconds.
Articles, 6 records found
Articles 6 records found  
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.
12 p, 490.1 KB Sur la systole de la sphère au voisinage de la métrique standard / Balacheff, Florent Nicolas (Université de Genève. Section de Mathématiques)
We study the systolic area (defined as the ratio of the area over the square of the systole) of the 2-sphere endowed with a smooth Riemannian metric as a function of this metric. This function, bounded from below by a positive constant over the space of metrics, admits the standard metric g 0 as a critical point, although it does not achieve the conjectured global minimum: we show that for each tangent direction to the space of metrics at g 0, there exists a variation by metrics corresponding to this direction along which the systolic area can only increase.
2006 - 10.1007/s10711-006-9087-7
Geometriae Dedicata, Vol. 121, Issue 1 (August 2006) , p. 61-71  
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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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4.
14 p, 380.7 KB Systoles and diameters of hyperbolic surfaces / Balacheff, Florent Nicolas (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Despré, Vincent (Université de Lorraine. Polytech Nancy) ; Parlier, Hugo (University of Luxembourg. Department of Mathematics)
In this article we explore the relationship between the systole and the diameter of closed hyperbolic orientable surfaces. We show that they satisfy a certain inequality, which can be used to deduce that their ratio has a (genus-dependent) upper bound.
2023 - 10.1215/21562261-2022-0040
Kyoto Journal of Mathematics, Vol. 63, Num. 1 (February 2023) , p. 211-222  
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5.
13 p, 322.0 KB A local optimal diastolic inequality on the two-sphere / Balacheff, Florent Nicolas (Université des Sciences et Technologies de Lille. Laboratoire Paul Painlevé)
We prove a local optimal inequality on the two-sphere between the area and the diastole - defined by a minimax process on the one-cycle space - in a neighborhood of the singular metric made of two equilateral triangles glued along their boundaries.
2010 - 10.1142/S1793525310000264
Journal of Topology and Analysis, Vol. 2, Num. 1 (March 2010) , p. 109-121  
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6.
13 p, 540.6 KB Volume entropy, weighted girths and stable balls on graphs / Balacheff, Florent Nicolas (University of Geneva. Department of Mathematics)
We prove new isoperimetric inequalities on graphs involving quantities linked with concepts from differential geometry. First, we bound from above the product of the volume entropy (defined as the log of the exponential growth rate of the universal cover) and the girth of weighted graphs in terms of their cyclomatic number. [...]
2007 - 10.1002/jgt.20236
Journal of Graph Theory, Vol. 55, Issue 4 (February 2007) , p. 291-305  
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