5 papers
Complete 3-manifolds of positive scalar curvature with quadratic decay
Florent Balacheff, Teo Gil Moreno de Mora SardÃ, 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…
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…
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…
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…