Geodesic
A characterization of shortest geodesics on surfaces
Neumann-Coto, Max1
1Instituto de Matemáticas UNAM, Ciudad Universitaria, México D.F. 04510, México
Algebraic and Geometric Topology, Tome 1 (2001) no. 1, pp. 349-368
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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.

DOI : 10.2140/agt.2001.1.349
Keywords: Surfaces, curves, geodesics, minimal intersections, metrics

Neumann-Coto, Max  1

1 Instituto de Matemáticas UNAM, Ciudad Universitaria, México D.F. 04510, México 
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Neumann-Coto, Max. A characterization of shortest geodesics on surfaces. Algebraic and Geometric Topology, Tome 1 (2001) no. 1, pp. 349-368. doi: 10.2140/agt.2001.1.349

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[5] M Shepard, PhD thesis, UC Berkeley (1990)

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