道路度量空间中的三角不等式
Triangle inequalities in path metric spaces
摘要：
研究了路度量空间中三角形的边长。证明了除非空间X是有界的，或与直线或半直线拟等距，否则满足严格三角不等式的实数三元组都是由X中三角形的边长实现的.我们构造了一个完备路径度量空间与欧氏平面拟等距的例子，其中每个退化三角形都有一条边短于某个一致常数。
英文摘要：
We study side-lengths of triangles in path metric spaces. We prove that unless such a space X is bounded, or quasi-isometric to line or half-line, 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 the Euclidean plane, for which every degenerate triangle has one side which is shorter than a certain uniform constant.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
