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A characterization of shortest geodesics on surfaces

Max Neumann-Coto

Algebraic & Geometric Topology 1 (2001) 349–368

arXiv: math.GT/0106200

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
Mathematical Subject Classification 2000
Primary: 53C22
Secondary: 53C42, 57R42
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Publication
Received: 8 January 2001
Accepted: 17 May 2001
Published: 2 June 2001
Authors
Max Neumann-Coto
Instituto de Matemáticas UNAM
Ciudad Universitaria
México D.F. 04510
México