Algebraic and Geometric Topology 1 (2001), paper no. 17, pages 349-368.

A characterization of shortest geodesics on surfaces

Max Neumann-Coto

Abstract. Any finite configuration of curves with minimal intersections on a surface is a configuration of shortest geodesics for some Riemannian metric on the surface. The metric can be chosen to make the lengths of these geodesics equal to the number of intersections along them.

Keywords. Surfaces, curves, geodesics, minimal intersections, metrics

AMS subject classification. Primary: 53C22. Secondary: 53C42,57R42.

DOI: 10.2140/agt.2001.1.349

E-print: arXiv:math.GT/0106200

Submitted: 8 January 2001. Accepted: 17 May 2001. Published: 2 June 2001.

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Max Neumann-Coto
Instituto de Matematicas UNAM,
Ciudad Universitaria, Mexico D.F. 04510, Mexico

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