双Lipschitz映射的一个充要条件  

A Sufficient and Necessary Condition for Bi-Lipschitz Maps

作　　者：陈克应[1] 

机构地区：[1]上海交通大学应用数学系,上海200240

出　　处：《上海交通大学学报》2002年第2期286-288,共3页Journal of Shanghai Jiaotong University

基　　金：国家自然科学基金 ( 195 310 6 0 );教育部博士点基金( 970 2 4811)

摘　　要：研究了 n-维 Euclid空间 (n≥ 2 )上的自同胚成为双 Lipschitz映射的充要条件 .运用曲线族的模和环模等工具 ,结合 Rohde定理 ,证明同胚为双 Lipschitz映射的充要条件是 :它适合环的对数绝对值不等式 ;还得到了同胚为拟共形映射的一个充分条件 .以上结果既是双 Lipschitz映射的一条深刻性质 ,又是它的一种新的几何刻划 .This paper studied the sufficient and necessary conditions for self homeomorphisms of n Euclidean spaces( n ≥2) to be bi Lipschitz maps. By applying the tools such as modulus of curves and rings, together with Rohde's theorem, it proves that a homeomorphism is a bi Lipschitz map if and only if it satisfies a logarithmically absolute value inequality of rings. Furtheremore, a sufficient condition for quasi conformal mappings is also obtained. Bi Lipschitz maps have been studied and applied by many mathematicans since they possess lots of perfect properties. Our result is a deep property and new geometric characterization of bi Lipschitz maps.

关 键 词：双Lipschitz映射 充要条件 模 拟共形映射 

分 类 号：O174.55[理学—数学]