46 citations · 131 across the 23 of their papers we have counts for
26 papers
Complete 3-manifolds of positive scalar curvature with quadratic decay
Florent Balacheff, Teo Gil Moreno de Mora Sardà, Stéphane Sabourau
We prove that if an orientable 3-manifold admits a complete Riemannian metric whose scalar curvature is positive and has a subquadratic decay at infinity, then it decomposes as…
Diastolic and isoperimetric inequalities on surfaces
Florent Balacheff, Stéphane Sabourau
We prove a universal inequality between the diastole, defined using a minimax process on the one-cycle space, and the area of closed Riemannian surfaces. Roughly speaking, we show…
A Basmajian-type inequality for Riemannian surfaces
Florent Balacheff, David Fisac
We explore for compact Riemannian surfaces whose boundary consists of a single closed geodesic the relationship between orthospectrum and boundary length. More precisely, we establ…
Short incompressible graphs and -free groups
Florent Balacheff, Wolfgang Pitsch
Consider a finite connected -complex endowed with a piecewise Riemannian metric and whose fundamental group is freely indecomposable, of rank at least , and in which ever…
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…
Isosystolic inequalities on two-dimensional Finsler tori
Florent Balacheff, Teo Gil Moreno de Mora
In this article we survey all known optimal isosystolic inequalities on two-dimensional Finsler tori involving the following two central notions of Finsler area: the Busemann-Hausd…
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…
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…
Macroscopic Schoen conjecture for manifolds with non-zero simplicial volume
Florent Balacheff, Steve Karam
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…
Length product of homologically independent loops for tori
Florent Balacheff, Steve Karam
We prove that any Riemannian torus of dimension with unit volume admits homologically independent closed geodesics whose length product is bounded from above by .
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…
Measurements of Riemannian two-disks and two-spheres
Florent Balacheff
We prove that any Riemannian two-sphere with area at most 1 can be continuously mapped onto a tree in a such a way that the topology of fibers is controlled and their length is les…
Isosystolic inequalities for optical hypersurfaces
Juan-Carlos Alvarez Paiva, Florent Balacheff, Kroum Tzanev
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 geometr…
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…
Contact geometry and isosystolic inequalities
Juan-Carlos Alvarez Paiva, Florent Balacheff
A long-standing open problem in systolic geometry asks whether a Riemannian metric on the real projective space whose volume equals that of the canonical metric, but is not isometr…
Short loop decompositions of surfaces and the geometry of Jacobians
Florent Balacheff, Hugo Parlier, Stéphane Sabourau
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 thr…
Systolic volume of homology classes
Ivan K. Babenko, Florent Balacheff
Given an integer homology class of a finitely presentable group, the systolic volume quantifies how tight could be a geometric realization of this class. In this paper, we study va…
Optimalité systolique infinitésimale de l'oscillateur harmonique
Juan-Carlos Álvarez Paiva, Florent Balacheff
We study the infinitesimal aspects of the following problem. Let H be a Hamiltonian of \R^{2n} whose energy surface {H=1} encloses a compact starshaped domain of volume equal to th…
Infinitesimal Systolic Rigidity of Metrics all of whose Geodesics are Closed and of the same Length
J. -C. Álvarez Paiva, F. Balacheff
The results of this paper have been greatly superseded by those in the paper "Contact geometry and isosystolic inequalities" (arXiv:1109.4253) by the same authors.
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…
A local optimal diastolic inequality on the two-sphere
Florent Balacheff
Using a ramified cover of the two-sphere by the torus, we prove a local optimal inequality between the diastole and the area on the two-sphere near a singular metric. This singular…
A Zoll counterexample to a geodesic length conjecture
Florent Balacheff, Christopher Croke, Mikhail G. Katz
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-sph…