Ricci curvature, the length of a shortest periodic geodesic and quantitative Morse theory on loop spaces

Abstract: I am planning to present the following result of mine: Let $M^n$ be a closed Riemannian manifold of dimension $n$ and $\operatorname{Ric} \geq (n−1)$. Then the length of a shortest periodic geodesic can be at most $8\pi n$.

The technique involves quantitative Morse theory on loop spaces. We will discuss some related results in geometry of loop spaces on Riemannian manifolds.

differential geometrygeometric topologymetric geometry

Audience: researchers in the topic

Topology and geometry: extremal and typical

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