46 citations · 122 across the 27 of their papers we have counts for
33 papers
Klein bottle and optimal systolic inequality for nonpositively curved surfaces
Mikhail G. Katz, Stephane Sabourau
We show that the systolic area of every nonpositively curved closed surface other than the torus is at least , with equality if and only if is isometric to a square flat…
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…
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…
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…
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…
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…