齐次完全集的拟对称极小性  

On the Quasisymmetric Minimality of Homogeneous Perfect Sets

作　　者：肖映青[1] 张展旗 Ying Qing XIAO;Zhan Qi ZHANG(College of Mathematics and Econometrics,Hunan University,Changsha 410082,P.R.China)

机构地区：[1]湖南大学数学与计量经济学院

出　　处：《数学学报（中文版）》2019年第4期573-590,共18页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11301165,11571099)

摘　　要：作为Cantor型集的推广,文志英和吴军引入了齐次完全集的概念,并基于齐次完全集的基本区间的长度以及基本区间之间的间隔的长度,得到了齐次完全集的Hausdorff维数.本文研究齐次完全集的拟对称极小性,证明在某些条件下Hausdorff维数为1的齐次完全集是1维拟对称极小的.Wen and Wu introduced the notion of homogeneous perfect sets as a generalization of Cantor type sets and determined their exact Hausdorff dimension based on the length of their basic intervals and the gaps between them. In this paper, we considered the quasisymmetrically minimality of the homogeneous perfect sets, proved the homogeneous perfect sets with Hausdorff dimension 1 are 1-dimensional quasisymmetrically minimal under some conditions.

关 键 词：齐次完全集 拟对称映射 拟对称极小集 

分 类 号：O174.12[理学—数学]