Self-contracted curves in Riemannian manifolds

Aris Daniilidis (1) , Robert . Deville (2) , Estibalitz Durand-Cartagena (3) , Ludovic Rifford (4)

1 UAB - Departament de Matemàtiques [Barcelona]
2 IMB - Institut de Mathématiques de Bordeaux
3 UNED - Universidad Nacional de Educación a Distancia
4 McTAO - Mathematics for Control, Transport and Applications

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

Mots clés: Length; Secant; Riemannian manifold; Self-contracted curve; Self-expanded curve; Rectifiable curve

Domaines: Analyse fonctionnelle [math.FA]

Aris Daniilidis, Robert . Deville, Estibalitz Durand-Cartagena, Ludovic Rifford. Self-contracted curves in Riemannian manifolds. Australian Journal of Mathematical Analysis and Applications, 2018, 457 (2), pp.1333-1352. ⟨10.1016/j.jmaa.2017.04.011⟩. ⟨hal-02478432⟩