凸域上拟双曲测地线直径的Gehring-Hayman恒等式  

The Gehring-Hayman identity for the diameter of quasihyperbolic geodesics in convex domain

作　　者：钱伟茂[1] 张益池[2] 

机构地区：[1]湖州广播电视大学远程教育学院,浙江湖州313000 [2]湖州职业技术学院机电工程学院,浙江湖州313000

出　　处：《纯粹数学与应用数学》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)

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Mbius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.

关 键 词：凸域 拟双曲长度 拟双曲距离 拟双曲测地线 Gehring-Hayman不等式 

分 类 号：O174.55[理学—数学]