The differential of a quasi-conformal mapping of a Carnot-Caratheodory space
The differential of a quasi-conformal mapping of a Carnot-Caratheodory space
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DOI：
10.1007/978-3-0348-9102-8_10
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发表时间：
1995-03
期刊：
影响因子：
--
通讯作者：
Gregory Margulis;G. Mostow
中科院分区：
文献类型：
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作者：
Gregory Margulis;G. Mostow
拟共形映射的理论已经被用来证明除代数Skn，Skn，Skn上双曲空间的刚性定理，并且通过研究其边界球Skn − 1上无穷远处的拟共形映射，其中Skn − 1是除代数的维数。这种空间的拟共形映射的概念，首先在[Mo 2]w中引入，随后由Pansu根据Carnot-Caratheodory空间M重新表述，Pansu研究了分次幂零群M的特殊情况下的拟共形映射。随后，Pansu的定义在[Mo 3]中被简化，而Koranyi-Reimann在研究复双曲空间边界上的幂零Heisenberg群的拟共形映射和在一点的补上的可迁映射时采用了这个更简单的定义。
The theory of quasi-conformal mappings has been used to prove rigidity theorems on hyperbolicnspace over the division algebrasℝ, ℂ, ℍ, and, by studying quasi-conformal mappings on their boundary spheresSkn−1at infinity, wherekis the dimension of the division algebra. The notion of quasiconformal mappings for such spaces, first introduced in [Mo2]w, as subsequently reformulated by Pansu in terms of Carnot-Caratheodory spacesM, and Pansu studied quasi-conformal mappings for the special case of graded nilpotent groupsM. Subsequently, Pansu’s definition was simplified in [Mo3], and this simpler definition was employed by Koranyi-Reimann in their study of quasi-conformal mappings of the nilpotent Heisenberg group operating on the boundary of complex hyperbolicn-space and transitive on the complement of one point.