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Dipòsit Digital de Documents de la UAB 33 registres trobats  1 - 10següentfinal  anar al registre: La cerca s'ha fet en 0.02 segons. 
1.
Projective transformations of convex bodies and volume product / Balacheff, Florent Nicolas (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Solanes, Gil (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Tzanev, Kroum (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper, we study certain variational aspects of the volume product functional restricted to the space of small projective deformations of a fixed convex body. In doing so, we provide a short proof of a theorem by Klartag: a strong version of the slicing conjecture implies the non-symmetric Mahler conjecture. [...]
2024 - 10.1093/imrn/rnad310
International Mathematics Research Notices  
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2.
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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3.
36 p, 942.1 KB Systolic geometry and simplicial complexity for groups / Babenko, Ivan (Université Montpellier II. Institut Montpelliérain Alexander Grothendieck) ; Balacheff, Florent Nicolas (Université de Lille. Laboratoire Paul Painlevé) ; Bulteau, Guillaume (Université Montpellier II. Institut Montpelliérain Alexander Grothendieck)
Twenty years ago Gromov asked about how large is the set of isomorphism classes of groups whose systolic area is bounded from above. This article introduces a new combinatorial invariant for finitely presentable groups called simplicial complexity that allows to obtain a quite satisfactory answer to his question. [...]
2019 - 10.1515/crelle-2017-0041
Journal fur die Reine und Angewandte Mathematik, Vol. 2019, Issue 757 (2019) , p. 247-277  
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4.
34 p, 1.1 MB Stable norms of non-orientable surfaces / Balacheff, Florent Nicolas (University of Neuchâtel. Department of Mathematics) ; Massart, Daniel (Université Montpellier II. Institut de Mathématiques et de Modélisation de Montpellier)
We study the stable norm on the first homology of a closed non-orientable surface equipped with a Riemannian metric. We prove that in every conformal class there exists a metric whose stable norm is polyhedral. [...]
2008 - 10.5802/aif.2386
Annales de l'Institut Fourier, Vol. 58, Num. 4 (2008) , p. 1337-1369  
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5.
39 p, 451.5 KB Isosystolic inequalities for optical hypersurfaces / Alvarez Paiva, Juan Carlos (Université de Lille. Laboratoire Paul Painlevé) ; Balacheff, Florent Nicolas (Université de Lille. Laboratoire Paul Painlevé) ; Tzanev, Kroum (Université de Lille. Laboratoire Paul Painlevé)
We explore a natural generalization of systolic geometry to Finsler metrics and optical hypersurfaces with special emphasis on its relation to the Mahler conjecture and the geometry of numbers. In particular, we show that if an optical hypersurface of contact type in the cotangent bundle of the 2-dimensional torus encloses a volume V, then it carries a periodic characteristic whose action is at most V/3. [...]
2016 - 10.1016/j.aim.2016.07.003
Advances in mathematics, Vol. 301 (October 2016) , p. 934-972  
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6.
21 p, 427.4 KB Macroscopic schoen conjecture for manifolds with nonzero simplicial volume / Balacheff, Florent Nicolas (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Karam, Steve (Lebanese University)
We prove that given a hyperbolic manifold endowed with an auxiliary Riemannian metric whose sectional curvature is negative and whose volume is sufficiently small in comparison to the hyperbolic one, we can always find for any radius at least 1 a ball in its universal cover whose volume is bigger than the hyperbolic one. [...]
2019 - 10.1090/tran/7765
Transactions of the American Mathematical Society, Vol. 372, Num. 10 (November 2019) , p. 7071-7086  
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7.
25 p, 464.2 KB The minimal length product over homology bases of manifolds / Balacheff, Florent Nicolas (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Karam, Steve (Lebanese University) ; Parlier, Hugo (University of Luxembourg. Department of Mathematics)
Minkowski's second theorem can be stated as an inequality for n-dimensional flat Finsler tori relating the volume and the minimal product of the lengths of closed geodesics which form a homology basis. [...]
2021 - 10.1007/s00208-021-02150-5
Mathematische Annalen, Vol. 380, Issue 1-2 (June 2021) , p. 825-854  
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8.
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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9.
20 p, 495.0 KB Géométrie systolique des sommes connexes et des revêtements cycliques / Babenko, Ivan (Université Montpellier II. Institut de Mathématiques et de Modélisation de Montpellier) ; Balacheff, Florent Nicolas (Université Montpellier II. Institut de Mathématiques et de Modélisation de Montpellier)
Nous étudions la constante systolique de la somme connexe de n exemplaires d'une variété M en fonction de ce nombre. Le comportement asymptotique de cette constante, connu dans le cas deux dimensionnel, demeure un problème ouvert dans les dimensions plus grandes que deux. [...]
2005 - 10.1007/s00208-005-0668-9
Mathematische Annalen, Vol. 333, Issue 1 (September 2005) , p. 157-180  
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10.
16 p, 496.2 KB Measurements of Riemannian two-disks and two-spheres / Balacheff, Florent Nicolas (Université de Lille. Laboratoire Paul Painlevé)
We prove that any Riemannian two-sphere having area at most 1 can be continuously mapped onto a tree in such a way that the topology of the fibers is controlled and their length is less than 7. 6. This result improves previous estimates and relies on a similar statement for Riemannian two-disks.
2015 - 10.2140/pjm.2015.275.167
Pacific Journal of Mathematics, Vol. 275, Num. 1 (April 2015) , p. 167-181  
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