Geometry and topology: my research interests lie in the area of metric geometry and quantitative topology, including global Riemannian geometry, hyperbolic geometry, geometric calculus of variations, geometric group theory, systolic geometry and asymptotic geometry.
Coordinator of the ANR project Min-max (ANR-19-CE40-0014): 2019-2023
Member of the ANR project Finsler (ANR-12-BS01-0009): 2012-2017
Ivan Babenko, Stéphane Sabourau, Volume entropy semi-norm and systolic volume semi-norm.
Journal of the European Mathematical Society, accepted for publication.
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Marcos Cossarini, Stéphane Sabourau, Minimal area of Finsler disks with minimizing geodesics.
Journal of the European Mathematical Society, accepted for publication.
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Stéphane Sabourau, Macroscopic scalar curvature and local collapsing.
Annales Scientifiques de l'École Normale Supérieure, vol. 55 (2022), no. 4, 919-936.
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Antonia Jabbour, Stéphane Sabourau, Sharp upper bounds on the length of the shortest closed geodesic on complete punctured spheres of finite area.
Revista Matemática Iberoamericana, vol. 38 (2022), no. 4, 1051-1065.
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Alexander Nabutovsky, Regina Rotman, Stéphane Sabourau, Sweepouts of closed Riemannian manifolds.
Geometric and Functional Analysis, vol. 31 (2021) 721-766.
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Mikhail Katz, Stéphane Sabourau, A Pu-Bonnesen inequality.
Journal of Geometry, vol. 112 (2021), no. 2, art. 18.
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Mikhail Katz, Stéphane Sabourau, Systolically extremal nonpositively curved surfaces are flat with finitely many singularities.
Journal of Topology and Analysis, vol. 13 (2021), no. 2, 319-347.
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Benoît Kloeckner, Stéphane Sabourau, Mixed sectional-Ricci curvature obstructions on tori.
Journal of Topology and Analysis, vol. 12 (2020), no. 3, 713-734.
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Stéphane Sabourau, One-cycle sweepout estimates of essential surfaces in closed Riemannian manifolds.
American Journal of Mathematics, vol. 142 (2020), no. 4, 1051-1082.
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Stéphane Sabourau, Strong deformation retraction of the space of Zoll Finsler projective planes.
Journal of Symplectic Geometry, vol. 17 (2019), no. 2, 443-476.
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Stéphane Sabourau, Zeina Yassine, A systolic-like extremal genus two surface.
Journal of Topology and Analysis, vol. 11 (2019), no. 3, 721-738.
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Stéphane Sabourau, Small volume of balls, large volume entropy and the Margulis constant.
Mathematische Annalen, vol. 369 (2017), no. 3-4, 1557-1571.
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Stéphane Sabourau, Volume of minimal hypersurfaces in manifolds with nonnegative Ricci curvature.
Journal für die reine und angewandte Mathematik (Crelle's Journal), vol. 731 (2017) 1-19.
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Stéphane Sabourau, Zeina Yassine, Optimal systolic inequalities on Finsler Mobius bands.
Journal of Topology and Analysis, vol. 8 (2016), no. 2, 349-372.
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Mikhail Katz, Stéphane Sabourau, Dyck's surfaces, systoles, and capacities.
Transactions of the American Mathematical Society, vol. 367 (2015), no. 6, 4483-4504.
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Stéphane Sabourau, Growth of quotients of groups acting by isometries on Gromov hyperbolic spaces.
Journal of Modern Dynamics, vol. 7 (2013), no. 2, 269-290.
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Mikhail Katz, Stéphane Sabourau, Hyperellipticity and systoles of Klein surfaces.
Geometriae Dedicata, vol. 159 (2012), no. 1, 277-293.
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Florent Balacheff, Hugo Parlier, Stéphane Sabourau, Short loop decompositions of surfaces and the geometry of Jacobians.
Geometric and Functional Analysis, vol. 22 (2012), no. 1, 37-73.
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Stéphane Sabourau, Isosystolic genus three surfaces critical for slow metric variations.
Geometry & Topology, vol. 15 (2011), no. 3, 1477-1508.
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Karin Katz, Mikhail Katz, Stéphane Sabourau, Steven Shnider, Shmuel Weinberger, Relative systoles of relative-essential 2-complexes.
Algebraic & Geometric Topology, vol. 11 (2011), no. 1, 197-217.
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Stéphane Sabourau, Local extremality of the Calabi-Croke sphere for the length of the shortest closed geodesic.
Journal of the London Mathematical Society, vol. 82 (2010), no. 3, 549-562.
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Aris Daniilidis, Olivier Ley, Stéphane Sabourau, Asymptotic behaviour of self-contracted planar curves and gradient orbits of convex functions.
Journal de Mathématiques Pures et Appliquées, vol. 94 (2010), no. 2, 183-199.
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Florent Balacheff, Stéphane Sabourau, Diastolic and isoperimetric inequalities on surfaces.
Annales Scientifiques de l'École Normale Supérieure, vol. 43 (2010), no. 4, 579-605.
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Stéphane Sabourau, Asymptotic bounds for separating systoles on surfaces.
Commentarii Mathematici Helvetici, vol. 83 (2008), no. 1, 35-54.
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Yuli Rudyak, Stéphane Sabourau, Systolic invariants of groups and 2-complexes via Grushko decomposition.
Annales de l'Institut Fourier, vol. 58 (2008), no. 3, 777-800.
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Stéphane Sabourau, Systolic volume of hyperbolic manifolds and connected sums of manifolds.
Geometriae Dedicata, vol. 127 (2007), no. 1, 7-18.
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Mikhail Katz, Yuli Rudyak, Stéphane Sabourau, Systoles of 2-complexes, Reeb graph, and Grushko decomposition.
International Mathematics Research Notices, (2006), Art. ID 54936, 30 pp.
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Stéphane Sabourau, Systolic volume and minimal entropy of aspherical manifolds.
Journal of Differential Geometry, vol. 74 (2006), no. 1, 155-176.
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Stéphane Sabourau, Entropy and systoles on surfaces.
Ergodic Theory and Dynamical Systems, vol. 26 (2006), no. 5, 1653-1669.
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Mikhail Katz, Stéphane Sabourau, An optimal systolic inequality for CAT(0) metrics in genus two.
Pacific Journal of Mathematics, vol. 227 (2006), no. 1, 95-107.
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Mikhail Katz, Stéphane Sabourau, Hyperelliptic surfaces are Loewner.
Proceedings of the American Mathematical Society, vol. 134 (2006), no. 4, 1189-1195.
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Mikhail Katz, Stéphane Sabourau, Entropy of systolically extremal surfaces and asymptotic bounds.
Ergodic Theory and Dynamical Systems, vol. 25 (2005), no. 4, 1209-1220.
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Stéphane Sabourau, Global and local volume bounds and the shortest geodesic loops.
Communications in Analysis and Geometry, vol. 12 (2004), no. 5, 1039-1053.
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Stéphane Sabourau, Filling radius and short closed geodesics of the 2-sphere.
Bulletin de la Société Mathématique de France, vol. 132 (2004), no. 1, 105-136.
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Stéphane Sabourau, Systoles des surfaces plates singulières de genre deux.
Mathematische Zeitschrift, vol. 247 (2004), no. 4, 693-709.
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Supervision
Ph.D. students:
Teo Gil Moreno de Mora Sardà (joint supervision with F. Balacheff), en cours.
Jean Chartier (joint supervision with L. Hauswirth and A. de Mesmay), Méthodes de min-max en géométrie : du continu au discret, soutenance prévue en 2024.
Elie Nakhle (joint supervision with M. Fradelizi), Conjecture de Mahler et dynamique du tore, soutenance prévue en 2023.
Antonia Jabbour, Inégalités systoliques optimales sur les surfaces, soutenue en 2022.
Zeina Yassine, Géométrie systolique extrémale sur les surfaces, soutenue en 2016.
Steve Karam, Croissance du volume des boules dans les revêtements universels des graphes
et des surfaces, soutenue en 2013.