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Articles, 3 records found
Articles 3 records found  
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  
Detailed record -
2.
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  
Detailed record - Creative Commons
3.
31 p, 522.8 KB The Santaló point for the Holmes-Thompson boundary area / Balacheff, Florent Nicolas (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Solanes, Gil (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Tzanev, Kroum (Université de Lille. Laboratoire Paul Painlevé)
We explore the notion of Santaló point for the Holmes-Thompson boundary area of a convex body in a normed space. In the case where the norm is C, and in the case where unit ball and convex body coincide, we prove existence and uniqueness. [...]
2021 - 10.1016/j.aim.2021.108118
Advances in mathematics, Vol. 397 (March 2022) , art. 108118  
Detailed record - Creative Commons

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