5 papers
Systole, inradius and rigidity of cusped hyperbolic 3-manifolds
Stephane Sabourau
We establish optimal inequalities relating the systole and the inradius to the volume of finite-volume hyperbolic 3-manifolds. In the cusped orientable case, we refine a theorem of…
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…
Nonpositively curved surfaces are Loewner
Mikhail G. Katz, Stephane Sabourau
We show that every closed nonpositively curved surface satisfies Loewner's systolic inequality. The proof relies on a combination of the Gauss-Bonnet formula with an averaging argu…
Logarithmic systolic growth for hyperbolic surfaces in every genus
Mikhail G. Katz, Stephane Sabourau
More than thirty years ago, Brooks and Buser-Sarnak constructed sequences of closed hyperbolic surfaces with logarithmic systolic growth in the genus. Recently, Liu and Petri showe…
Minimal volume entropy and fiber growth
Ivan Babenko, Stéphane Sabourau
This article deals with topological assumptions under which the minimal volume entropy of a closed manifold , and more generally of a finite simplicial complex , vanishes or…