A LOCAL OPTIMAL DIASTOLIC INEQUALITY ON THE TWO-SPHERE

DOI10.1142/S1793525310000264zbMath1193.53105arXiv0811.0330OpenAlexW1964622977MaRDI QIDQ3560118

Florent Balacheff

Publication date: 19 May 2010

Published in: Journal of Topology and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0811.0330

zbMATH Keywords

systoleCalabi's conjectureramified coverconical singularity, diastole, two-sphere

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)

Related Items (9)

Sharp upper bounds on the length of the shortest closed geodesic on complete punctured spheres of finite area ⋮ Volume of minimal hypersurfaces in manifolds with nonnegative Ricci curvature ⋮ Relative systoles of relative-essential 2-complexes ⋮ Isosystolic genus three surfaces critical for slow metric variations ⋮ The length of a shortest closed geodesic on a surface of finite area ⋮ A systolic inequality for geodesic flows on the two-sphere ⋮ Hurwitz quaternion order and arithmetic Riemann surfaces ⋮ A systolic inequality with remainder in the real projective plane ⋮ A systolic-like extremal genus two surface

Cites Work

• Unnamed Item
• On the systole of the sphere in the proximity of the standard metric
• Simple closed geodesics on convex surfaces
• The homotopy groups of the integral cycle groups
• Some inequalities in certain nonorientable Riemannian manifolds
• Differential Topology
• The length of a shortest closed geodesic and the area of a 2-dimensional sphere

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