From the Poincaré "lignes de partages" to the convex earth theorem
1,052 views · Published 28 May 2013 · 50:17 · Indexed 13 October 2026
Channel: Institut Henri Poincaré · 2013 · Science & Technology
By Ludovic RiffordAbstract: The cut locus of a complete Riemannian manifold goes back to the "Lignes de partage" which have been defined by Poincaré in his celebrated 1905 paper "Sur les lignes géodésiques des surfaces convexes". Given a point P on a (complete) Riemannian manifold, the cut locus from P is defined as the closure of the set of points which can be joined to P with at least two minimizing geodesics. The purpose of this talk is to review some of the results which have been obtained since the Poincaré paper concerning the structure, the size, or the curvature of the cut locus. Note(s) Biographique(s) Ludovic Rifford est diplômé de l'Université Claude Bernard Lyon 1 dont il fut diplômé en 2000. Ses thèmes de recherche sont l'analyse, la théorie géométrique du contrôle, la géométrie sous-riemannienne, le transport optimal, la dynamique hamiltonienne. Il est membre junior de l'Institut Universitaire de France. Réalisation : Quentin Lazzarotto Date : 23/11/2012 Lieu : Institut Henri Poincaré
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