Upper bounds on the length of a shortest closed geodesic and quantitative Hurewicz theorem

DOI10.1007/s10097-003-0051-7zbMath1039.53042OpenAlexW2042537709MaRDI QIDQ1409588

Regina Rotman, Alexander Nabutovsky

Publication date: 16 October 2003

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10097-003-0051-7

zbMATH Keywords

volumediametersectional curvatureshortest closed geodesicsmallest non-contractible \(k\)-dimensional sphere

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22)

Related Items

Length of geodesics and quantitative Morse theory on loop spaces, Length of a shortest closed geodesic in manifolds of dimension four, Contact geometry and isosystolic inequalities, Singularities, expanders and topology of maps. II: From combinatorics to topology via algebraic isoperimetry, An upper bound for the smallest area of a minimal surface in manifolds of dimension four

Cites Work

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• Existence of closed geodesics on positively curved manifolds
• Filling Riemannian manifolds
• Area and the length of the shortest closed geodesic
• Bounding homotopy types by geometry
• Homotopical effects of dilatation
• Some isoperimetric inequalities and eigenvalue estimates
• Lectures on Morse theory, old and new
• Finiteness Theorems for Riemannian Manifolds
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu