Bilipschitz embedding of self-similar sets

Journal d'Analyse Mathematique

Volumn 114, Issue 1, 2011, Pages 63-97

  Deng, Juan ^a   Wen, Zhi ying ^a   Xiong, Ying ^b   Xi, Li Feng ^c  

^a TSINGHUA UNIVERSITY   (China)

^b SOUTH CHINA UNIVERSITY OF TECHNOLOGY   (China)

^c Zhejiangwanli University Ningbo   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 80052943601     PISSN: 00217670     EISSN: 15658538     Source Type: Journal    
DOI: 10.1007/s11854-011-0012-0     Document Type: Article

References (26)

1. M. Bonk, Quasiconformal geometry of fractals, International Congress of Mathematicians, vol. II, Eur. Math. Soc., Zürich, 2006, pp.-1349-1373.
2. D. Cooper and T. Pignataro, On the shape of Cantor sets, J. Differential Geom. 28 (1988), 203-221.
3. G. David and S. Semmes, Fractured Fractals and Broken Dreams, Oxford University Press, New York, 1997.
4. K. J. Falconer, Techniques in Fractal Geometry, John Wiley & Sons, Ltd., Chichester, 1997.
5. K. J. Falconer, Dimensions and measures of quasi self-similar sets, Proc. Amer. Math. Soc. 106 (1989), 543-554.
6. K. J. Falconer and D. T. Marsh, Classification of quasi-circles by Hausdorff dimension, Nonlinearity 2 (1989), 489-493.
7. K. J. Falconer and D. T. Marsh, On the Lipschitz equivalence of Cantor sets, Mathematika 39 (1992), 223-233.
8. B. Farb and L. Mosher, A rigidity theorem for the solvable Baumslag-Solitar groups, Invent. Math. 131 (1998) 419-451.
9. J. E. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J. 30 (1981), 713-747.
10. R. Kenyon, Projecting the one-dimensional Sierpinski gasket, Israel J. Math. 97 (1997), 221-238.
11. M. Llorente and P. Mattila, Lipschitz equivalence of subsets of self-conformal sets, Nonlinearity 23 (2010), 875-882.
12. P. Mattila, Geometry of Sets and Measures in Euclidean Spaces, Cambridge University Press, 1995.
13. P. Mattila and P. Saaranen, Ahlfors-David regular sets and bilipschitz maps, Ann. Acad. Sci. Fenn. Math. 34 (2009), 487-502.
14. P. A. P. Moran, Additive functions of intervals and Hausdorff measure, Proc. Cambridge Philos. Soc. 42 (1946), 15-23.
15. R. D. Mauldin and S. C. Williams, Hausdorff dimension in graph directed constructions, Trans. Amer. Math. Soc. 309 (1988), 811-839.
16. H. Rao, H. J. Ruan, and L. F. Xi, Lipschitz equivalence of self-similar sets, C. R. Math. Acad. Sci. 342 (2006), 191-196.
17. H. J. Ruan and L. F. Xi, Lipschitz equivalence of self-similar sets with touching structure, preprint.
18. A. Schief, Separation properties for self-similar sets, Proc. Amer. Math. Soc. 122 (1994), 111-115.
19. Z. Y. Wen, Moran sets and Moran classes, Chinese Sci. Bull. 46 (2001), 1849-1856.
20. Z. Y. Wen and L. F. Xi, Relations among Whitney sets, self-similar arcs and quasi-arcs, Israel J. Math. 136 (2003), 251-267.
21. L. F. Xi, Lipschitz equivalence of self-conformal sets, J. LondonMath. Soc. 70 (2004), 369-382.
22. L. F. Xi, Quasi-Lipschitz equivalence of fractals, Israel J. Math. 160 (2007), 1-21.
23. L. F. Xi, Lipschitz equivalence of dust-like self-similar sets, Math. Z. 266 (2010), 683-691.
24. L. F. Xi and H. J. Ruan, Lipschitz equivalence of generalized {1, 3, 5, }-{1, 4, 5} self-similar sets, Sci. China Ser. A 50 (2007), 1537-1551.
25. L. F. Xi and Y. Xiong, Lipschitz equivalence of graph-directed fractals, Studia Math. 194 (2009), 197-205.
26. L. F. Xi and Y. Xiong, Self-similar sets with initial cubic patterns, C. R. Math. Acad. Sci. 348 (2010), 15-20.