Abstract
We study side-lengths of triangles in path metric spaces. We prove that unless such a space is bounded, or quasi-isometric to or to , every triple of real numbers satisfying the strict triangle inequalities, is realized by the side-lengths of a triangle in . We construct an example of a complete path metric space quasi-isometric to for which every degenerate triangle has one side which is shorter than a certain uniform constant.
Citation
Michael Kapovich. "Triangle inequalities in path metric spaces." Geom. Topol. 11 (3) 1653 - 1680, 2007. https://doi.org/10.2140/gt.2007.11.1653
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