English

Bilipschitz embedding of homogeneous fractals

Metric Geometry 2014-09-16 v4

Abstract

In this paper, we introduce a class of fractals named homogeneous sets based on some measure versions of homogeneity, uniform perfectness and doubling. This fractal class includes all Ahlfors-David regular sets, but most of them are irregular in the sense that they may have different Hausdorff dimensions and packing dimensions. Using Moran sets as main tool, we study the dimensions, bilipschitz embedding and quasi-Lipschitz equivalence of homogeneous fractals.

Keywords

Cite

@article{arxiv.1402.0080,
  title  = {Bilipschitz embedding of homogeneous fractals},
  author = {Fan Lü and Man-Li Lou and Zhi-Ying Wen and Li-Feng Xi},
  journal= {arXiv preprint arXiv:1402.0080},
  year   = {2014}
}
R2 v1 2026-06-22T02:59:05.227Z