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math.MG2023
Projective transformations of convex bodies and volume product
Florent Balacheff, Gil Solanes, Kroum Tzanev
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…
math.MG2020★ 1 cited
The Santaló point for the Holmes-Thompson boundary area
Florent Balacheff, Gil Solanes, Kroum Tzanev
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 , and in the case where unit bal…
math.MG2004★ 4 cited
Volume entropy, systole and stable norm on graphs
Florent Balacheff
We study some new isoperimetric inequalities on graphs. We etablish a relation between the volume entropy (or asymptotic volume), the systole and the first Betti number of weighted…