Gromov Hyperbolic Discrete Spaces and Their Application to Extension of Classes of Mappings

被引:1
|
作者
Trotsenko, D. A. [1 ]
机构
[1] Russian Acad Sci, Sobolev Inst Math, Siberian Branch, Novosibirsk 630090, Russia
关键词
QUASI-SYMMETRIC MAPS; SETS; BILIPSCHITZ;
D O I
10.1134/S1064562411030240
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Gromov hyperbolic discrete spaces and their application to extension of classes of mappings are studied. A metric space is considered and the equality relation between sequences is defined. The extendability of a mapping requires the compatibility of its approximations in the sense that the characteristics of the corresponding standard mappings on sufficiently close balls must be close. If a mapping is approximated by similarities on each ball, the quasiconformal extendability of this mapping requires that the angle of rotation and the logarithm of the coefficient of pressure must satisfy the weak condition. For a quasiconvex metric space, function with the weak property is found to be near-Lipschitz. For quasi-convex space and a function with extendability property, a space exists with intrinsic metric.
引用
收藏
页码:344 / 347
页数:4
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