Decomposing multitwists
Decomposing multitwists
复制标题
分解多重扭曲
DOI：
10.1007/s11854-023-0301-4
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Vyron Vellis
中科院分区：
文献类型：
--
作者：
A. Fletcher;Vyron Vellis
类$$LIP({\mathbb{S}^2})$$ L I P （s2）中的分解问题是将任意bi-Lipschitz映射$$f:{\mathbb{S}^2} \to {\mathbb{S}^2}$$ f: s2→s2分解为具有任意小等长畸变的有限多个映射的组合。本文构造了一类双lipschitz映射的分解，这些映射绕着一个维数严格小于1的康托集合X的每一点旋转。这些地图是通过考虑黎曼表面$${\mathbb{S}^2}\backslash X$$ s2 X上的Dehn扭曲的集合来构建的。然后通过双利普希茨路径获得分解，该路径同时解开这些Dehn扭曲。作为构造的一部分，我们还证明$$X \subset {\mathbb{S}^2}$$ X≠s2是均匀断开的，当且仅当黎曼曲面$${\mathbb{S}^2}\backslash X$$ S≠X有一个裤子分解，其袖口的双曲长度在上面均匀有界，这可能是独立的兴趣。
The Decomposition Problem in the class $$LIP({\mathbb{S}^2})$$ L I P ( S 2 ) is to decompose any bi-Lipschitz map $$f:{\mathbb{S}^2} \to {\mathbb{S}^2}$$ f : S 2 → S 2 as a composition of finitely many maps of arbitrarily small isometric distortion. In this paper, we construct a decomposition for certain bi-Lipschitz maps which spiral around every point of a Cantor set X of Assouad dimension strictly smaller than one. These maps are constructed by considering a collection of Dehn twists on the Riemann surface $${\mathbb{S}^2}\backslash X$$ S 2 \ X . The decomposition is then obtained via a bi-Lipschitz path which simultaneously unwinds these Dehn twists. As part of our construction, we also show that $$X \subset {\mathbb{S}^2}$$ X ⊂ S 2 is uniformly disconnected if and only if the Riemann surface $${\mathbb{S}^2}\backslash X$$ S 2 \ X has a pants decomposition whose cuffs have hyperbolic length uniformly bounded above, which may be of independent interest.
影响因子：
0.9
作者：
Fletcher A
通讯作者：
Fletcher A
具有有界几何的康托集的均匀化
DOI：
10.1090/ecgd/360
发表时间：
2021
期刊：
Conformal Geometry and Dynamics of the American Mathematical Society
影响因子：
--
作者：
Vellis, Vyron
通讯作者：
Vellis, Vyron