Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 759-769

QUASI-LIPSCHITZ EQUIVALENCE OF SUBSETS OF AHLFORS-DAVID REGULAR SETS

Qiuli Guo, Hao Li and Qin Wang

Zhejiang Wanli University, Institute of Mathematics
Ningbo, Zhejiang, 315100, P.R. China; guoqiuli 'at' zwu.edu.cn

Zhejiang Wanli University, Institute of Mathematics
Ningbo, Zhejiang, 315100, P.R. China; kevinlee9809 'at' hotmail.com

Zhejiang Wanli University, School of Computer Science and Information Technology
Ningbo, Zhejiang, 315100, P.R. China; qinwang 'at' 126.com

Abstract. In the paper, it is proved that for any Ahlfors-David s-regular sets E and F in Euclidean spaces, there exist subsets E' \subset E and F' \subset F such that dim_HE' = dim_HF' = s and E', F' are quasi-Lipschitz equivalent.

2010 Mathematics Subject Classification: Primary 28A80.

Key words: Fractal, Ahlfors-David regularity, quasi-Lipschitz equivalence, Moran set.

Reference to this article: Q. Guo, H. Li and Q. Wang: Quasi-Lipschitz equivalence of subsets of Ahlfors-David regular sets. Ann. Acad. Sci. Fenn. Math. 39 (2014), 759-769.

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doi:10.5186/aasfm.2014.3930