The length of a shortest closed geodesic and the area of a 2-dimensional sphere

DOI10.1090/S0002-9939-06-08297-9zbMath1098.53035OpenAlexW1484506367MaRDI QIDQ5473433

Regina Rotman

Publication date: 21 June 2006

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-06-08297-9

zbMATH Keywords

areaRiemannian manifoldclosed geodesicgeometric inequality

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)

Related Items (18)

Convergence and the length spectrum ⋮ Isosystolic inequalities for optical hypersurfaces ⋮ Geodesic loops and periodic geodesics on a Riemannian manifold diffeomorphic to \(S^{3}\) ⋮ Sharp upper bounds on the length of the shortest closed geodesic on complete punctured spheres of finite area ⋮ On the systole of the sphere in the proximity of the standard metric ⋮ Length of a shortest closed geodesic in manifolds of dimension four ⋮ The length of a shortest closed geodesic on a surface of finite area ⋮ Contact geometry and isosystolic inequalities ⋮ A LOCAL OPTIMAL DIASTOLIC INEQUALITY ON THE TWO-SPHERE ⋮ A systolic inequality for geodesic flows on the two-sphere ⋮ Minimizing closed geodesics on polygons and disks ⋮ An inequality for length and volume in the complex projective plane ⋮ Sharp systolic inequalities for Riemannian and Finsler spheres of revolution ⋮ The length of the shortest closed geodesic in a closed Riemannian 3-manifold with nonnegative Ricci curvature ⋮ Short geodesic loops on complete Riemannian manifolds with a finite volume ⋮ The minimal length of a closed geodesic net on a Riemannian manifold with a nontrivial second homology group ⋮ Open problems and questions about geodesics ⋮ Slicing a 2-sphere

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