Algebraic & Geometric Topology 1 (2001) 349–368

DOI: 10.2140/agt.2001.1.349

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

Primary: 53C22

Secondary: 53C42, 57R42

References

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Publication

Received: 8 January 2001
Accepted: 17 May 2001
Published: 2 June 2001

Authors