Annales Academić Scientiarum Fennicć
Mathematica
Volumen 36, 2011, 139-151

QUASISYMMETRICALLY MINIMAL MORAN SETS AND HAUSDORFF DIMENSION

Yuxia Dai, Zhixiong Wen, Lifeng Xi and Ying Xiong

Huazhong University of Science and Technology, Department of Mathematics
Wuhan 430074, P.R. China; daiyuxia8173 'at' 163.com

Huazhong University of Science and Technology, Department of Mathematics
Wuhan 430074, P.R. China; zhi-xiong.wen 'at' mail.hust.edu.cn

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

South China University of Technology, Department of Mathematics
Guangzhou 510641, P.R. China; xiongyng 'at' gmail.com

Abstract. In this paper, we prove that a large class of Moran sets on the line with Hausdorff dimension 1 are 1-dimensional quasisymmetrically minimal. We also obtain a general theorem on the Hausdorff dimension of Moran set on the line.

2000 Mathematics Subject Classification: Primary 30C65; Secondary 28A80.

Key words: Quasisymmetrically minimal set, Moran set, Hausdorff dimension, Gibbs-like measure.

Reference to this article: Y. Dai, Z. Wen, L. Xi and Y. Xiong: Quasisymmetrically minimal Moran sets and Hausdorff dimension. Ann. Acad. Sci. Fenn. Math. 36 (2011), 139-151.

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doi:10.5186/aasfm.2011.3608