Triangle inequalities in path metric spaces
نویسنده
چکیده
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.
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