46 citations · 122 across the 27 of their papers we have counts for
25 papers · 1 filter
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…
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…
Sharp reverse isoperimetric inequalities in nonpositively curved cones
Mikhail G. Katz, Stephane Sabourau
We prove a pair of sharp reverse isoperimetric inequalities for domains in nonpositively curved surfaces: (1) metric disks centered at the vertex of a Euclidean cone of angle at le…
Sharp upper bounds on the length of the shortest closed geodesic on complete punctured spheres of finite area
Antonia Jabbour, Stéphane Sabourau
We establish sharp universal upper bounds on the length of the shortest closed geodesic on a punctured sphere with three or four ends endowed with a complete Riemannian metric of f…
Sweepouts of closed Riemannian manifolds
Alexander Nabutovsky, Regina Rotman, Stéphane Sabourau
We show that for every closed Riemannian manifold there exists a continuous family of -cycles (defined as finite collections of disjoint closed curves) parametrized by a sphere…
Macroscopic scalar curvature and local collapsing
Stéphane Sabourau
Consider a closed Riemannian -manifold admitting a negatively curved Riemannian metric. We show that for every Riemannian metric on of sufficiently small volume, there i…
Systolically extremal nonpositively curved surfaces are flat with finitely many singularities
Mikhail Katz, Stephane Sabourau
The regularity of systolically extremal surfaces is a notoriously difficult problem already discussed by M. Gromov in 1983, who proposed an argument toward the existence of -e…
Mixed sectional-Ricci curvature obstructions on tori
Benoît Kloeckner, Stéphane Sabourau
We establish new obstruction results to the existence of Riemannian metrics on tori satisfying mixed bounds on both their sectional and Ricci curvatures. More precisely, from Lohka…
Strong deformation retraction of the space of Zoll Finsler projective planes
Stéphane Sabourau
We show that the infinite-dimensional space of Zoll Finsler metrics on the projective plane strongly deformation retracts to the canonical round metric. In particular, this space o…
Optimal systolic inequalities on Finsler Mobius bands
Stéphane Sabourau, Zeina Yassine
We prove optimal systolic inequalities on Finsler Mobius bands relating the systole and the height of the Mobius band to its Holmes-Thompson volume. We also establish an optimal sy…
Volume of minimal hypersurfaces in manifolds with nonnegative Ricci curvature
Stéphane Sabourau
We establish a min-max estimate on the volume width of a closed Riemannian manifold with nonnegative Ricci curvature. More precisely, we show that every closed Riemannian manifold…
Dyck's surfaces, systoles, and capacities
Mikhail G. Katz, Stephane Sabourau
We prove an optimal systolic inequality for nonpositively curved Dyck's surfaces. The extremal surface is flat with eight conical singularities, six of angle theta and two of angle…
Hyperellipticity and Systoles of Klein Surfaces
Mikhail G. Katz, Stephane Sabourau
Given a hyperelliptic Klein surface, we construct companion Klein bottles, extending our technique of companion tori already exploited by the authors in the genus 2 case. Bavard's…
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…
Relative systoles of relative-essential 2-complexes
Karin U. Katz, Mikhail G. Katz, Stephane Sabourau +2
We prove a systolic inequality for the phi-relative 1-systole of a phi-essential 2-complex, where phi is a homomorphism from the fundamental group of the complex, to a finitely pre…
Local extremality of the Calabi-Croke sphere for the length of the shortest closed geodesic
Stephane Sabourau
Recently, F. Balacheff proved that the Calabi-Croke sphere made of two flat 1-unit-side equilateral triangles glued along their boundaries is a local extremum for the length of the…
Systolic invariants of groups and 2-complexes via Grushko decomposition
Yuli B. Rudyak, Stéphane Sabourau
We prove a finiteness result for the systolic area of groups, answering a question of M. Gromov. Namely, we show that there are only finitely many possible unfree factors of fundam…
Systolic volume and minimal entropy of aspherical manifolds
Stephane Sabourau
We establish isosystolic inequalities for a class of manifolds which includes the aspherical manifolds. In particular, we relate the systolic volume of aspherical manifolds first t…
Systoles of 2-complexes, Reeb graph, and Grushko decomposition
Mikhail G. Katz, Yuli B. Rudyak, Stephane Sabourau
Let X be a finite 2-complex with unfree fundamental group. We prove lower bounds for the area of a metric on X, in terms of the square of the least length of a noncontractible loop…
An optimal systolic inequality for CAT(0) metrics in genus two
Mikhail G. Katz, Stephane Sabourau
We prove an optimal systolic inequality for CAT(0) metrics on a genus~2 surface. We use a Voronoi cell technique, introduced by C.~Bavard in the hyperbolic context. The equality is…
Entropy of systolically extremal surfaces and asymptotic bounds
Mikhail G. Katz, Stephane Sabourau
We find an upper bound for the entropy of a systolically extremal surface, in terms of its systole. We combine the upper bound with A. Katok's lower bound in terms of the volume, t…