46 citations · 131 across the 23 of their papers we have counts for
6 papers · 1 filter
Systoles and diameters of hyperbolic surfaces
Florent Balacheff, Vincent Despré, Hugo Parlier
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…
A curvature-free Log(2k-1) Theorem
Florent Balacheff, Louis Merlin
This paper presents a curvature-free version of the Log(2k-1) Theorem of Anderson, Canary, Culler & Shalen [ACCS96]. It generalizes a result by Hou [Hou01] and its proof is rather…
Minimal length product over homology bases of manifolds
Florent Balacheff, Steve Karam, Hugo Parlier
Minkowski's second theorem can be stated as an inequality for -dimensional flat Finsler tori relating the volume and the minimal product of the lengths of closed geodesics which…
Systolic geometry and simplicial complexity for groups
Ivan Babenko, Florent Balacheff, Guillaume Bulteau
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 inv…
Systole growth for finite area hyperbolic surfaces
Florent Balacheff, Eran Makover, Hugo Parlier
We are interested in the maximum value achieved by the systole function over all complete finite area hyperbolic surfaces of a given signature . This maximum is shown to be…
Bers' constants for punctured spheres and hyperelliptic surfaces
Florent Balacheff, Hugo Parlier
This article is dedicated to prove Buser's conjecture about Bers' constants for spheres with cusps (or marked points) and for hyperelliptic surfaces. More specifically, our main th…