摘要
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Mbius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 MSbius 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.
出处
《纯粹数学与应用数学》
CSCD
2013年第3期241-245,274,共6页
Pure and Applied Mathematics
基金
浙江省自然科学基金(LY13A010004)
国家开放大学基金(Q1601E-Y)
浙江省教育厅基金(Y201223519)
