Sharp upper bounds on the length of the shortest closed geodesic on complete punctured spheres of finite area

DOI10.4171/RMI/1362zbMath1505.53057arXiv2009.10144OpenAlexW3087865617WikidataQ114021378 ScholiaQ114021378MaRDI QIDQ2157352

Antonia Jabbour, Stéphane Sabourau

Publication date: 27 July 2022

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.10144

zbMATH Keywords

extremal metricspunctured spheresramified coversnoncompact surfacesshortest closed geodesicoptimal systolic inequalities

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Critical metrics (58E11) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60)

Related Items

Extending Gromov's optimal systolic inequality

Cites Work

• Isosystolic inequalities for optical hypersurfaces
• Short loop decompositions of surfaces and the geometry of Jacobians
• Isosystolic genus three surfaces critical for slow metric variations
• Convex programs for minimal-area problems
• Minimal-area metrics on the Swiss cross and punctured torus
• Filling Riemannian manifolds
• Inégalité isosystolique pour la bouteille de Klein. (Isosystolic inequalities for the Klein bottle)
• Area and the length of the shortest closed geodesic
• Closed geodesics on complete surfaces
• Some lower bounds for the area of surfaces
• Closed geodesics on non-compact Riemannian manifolds
• An optimal systolic inequality for \(\mathrm{CAT}(0)\) metrics in genus two
• Some inequalities in certain nonorientable Riemannian manifolds
• Local extremality of the Calabi-Croke sphere for the length of the shortest closed geodesic
• A LOCAL OPTIMAL DIASTOLIC INEQUALITY ON THE TWO-SPHERE
• A volume comparison theorem for Finsler manifolds
• Filling Radius and Short Closed Geodesics of the $2$-Sphere
• Open problems and questions about geodesics
• The length of a shortest closed geodesic on a surface of finite area
• Systolically extremal nonpositively curved surfaces are flat with finitely many singularities
• A systolic-like extremal genus two surface
• Dyck’s surfaces, systoles, and capacities
• The length of a shortest closed geodesic and the area of a 2-dimensional sphere
• Entropy of systolically extremal surfaces and asymptotic bounds
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item