Geodesic
Triangle inequalities in path metric spaces
Kapovich, Michael1
1 Department of Mathematics, University of California, Davis, Davis CA 95616, USA
Geometry & topology, Tome 11 (2007) no. 3, pp. 1653-1680.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We study side-lengths of triangles in path metric spaces. We prove that unless such a space X is bounded, or quasi-isometric to ℝ+ or to ℝ, every triple of real numbers satisfying the strict triangle inequalities, is realized by the side-lengths of a triangle in X. We construct an example of a complete path metric space quasi-isometric to ℝ2 for which every degenerate triangle has one side which is shorter than a certain uniform constant.

DOI : 10.2140/gt.2007.11.1653
Keywords: path metric spaces, triangles

Kapovich, Michael 1

1 Department of Mathematics, University of California, Davis, Davis CA 95616, USA 
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Kapovich, Michael. Triangle inequalities in path metric spaces. Geometry & topology, Tome 11 (2007) no. 3, pp. 1653-1680. doi : 10.2140/gt.2007.11.1653. http://geodesic.mathdoc.fr/articles/10.2140/gt.2007.11.1653/

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