Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 42, No. 2, pp. 595-599 (2001)

Courbes et polygones faiblement convexes en courbure strictement négative pincée

Stéphane Grognet

Département de Mathématiques, Université de Nantes, U. M. R. 6629, 2, rue de la Houssiniere, BP 92208, F-44322 Nantes cedex 03, e-mail:

Abstract: Some curves with low geodesic curvature on a connected, simply connected riemannian manifold with pinched negative curvature happen to be weakly convex. It results that on a surface with $1/4$-pinched negative curvature, the bisectors and Dirichlet domains of discrete groups of isometries with a finite number of faces are weakly convex.

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