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Self-contracted curves in Riemannian manifolds

Authors:	Aris Daniilidis Robert Deville Estibalitz Durand-Cartagena Ludovic Rifford

Institution:	1. DIM–CMM, UMI CNRS 2807, Beauchef 581, Torre Norte, piso 5, Universidad de Chile, Santiago 8370456, Chile;2. Laboratoire Bordelais d''Analyse et Geométrie, Institut de Mathématiques de Bordeaux, Université de Bordeaux 1, 351 cours de la Libération, Talence Cedex 33405, France;3. Departamento de Matemática Aplicada, ETSI Industriales, UNED, Juan del Rosal 12, Ciudad Universitaria, 28040 Madrid, Spain;5. Laboratoire J.A. Dieudonné, UMR CNRS 7351, Université Nice Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 2, France

Abstract:	It is established that every self-contracted curve in a Riemannian manifold has finite length, provided its image is contained in a compact set.

Keywords:	Self-contracted curve Self-expanded curve Rectifiable curve Length Secant Riemannian manifold
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