将平面 Jordan 域上关于双曲测地线直径的 Gehring-Hayman 不等式推广到 n维空间凸域上的拟双曲测地线。利用 M¨obius 变换和拟双曲度量证明了 n 维空间凸域上连接任意二点 x 和 y 的拟双曲测地线的直径等于 x 与 y 之间的 Euclidean 距离。所得结果推广和改进了相关已有结果。% Generalize the Gehring-Hayman inequality for the diameter of the hyperbolic geodesics in the plane Jordan domain to the quasihyperbolic geodesics in the convex domain of n-dimensional space. Making use of the M¨obius transformation and the quasihyperbolic metric, we prove that the diameter of the quasihyperbolic geodesics with the endpoints x and y in the convex domain of n-dimensional space is equal to the Euclidean distance between x and y. The obtained result is a generalization and improvement of some known results.
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