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arXiv · 2203.14051

Upper bounds for the critical values of homology classes of loops

Hans-Bert Rademacher
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Abstract

In this short note we discuss upper bounds for the critical values of homology classes in the based and free loop space of manifolds carrying a Riemannian or Finsler metric of positive Ricci curvature. In particular it follows that a shortest closed geodesic on a simply-connected $n$-dimensional manifold of positive Ricci curvature $\textrm{Ric} \ge n-1$ has length $\le n \pi.$

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Hans-Bert Rademacher. 2022-03-26. Upper bounds for the critical values of homology classes of loops. https://arxiv.org/abs/2203.14051

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