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Hausdorff Dimensions of Quasilines and Differentiability of Quasisymmetric Homeomorphisms

Hausdorff Dimensions of Quasilines and Differentiability of Quasisymmetric Homeomorphisms
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摘要 In this paper,we try to describe the relationship between the differentiability of a quasisymmetric homeomorphism and the local Hausdorff dimension of the quasiline at a point. In this paper,we try to describe the relationship between the differentiability of a quasisymmetric homeomorphism and the local Hausdorff dimension of the quasiline at a point.
作者 Sheng Jin HUO Sheng Jian WU
机构地区 Department of Mathematics LMAM and School of Mathematical Sciences
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2016年第4期499-506,共8页 数学学报（英文版）
基金 supported by National Natural Science Foundation of China(Grant Nos.11401432 and11571172) the second author is supported by National Natural Science Foundation of China(Grant No.11371035)
关键词 Quasiline quasisymmetric Fuchsian group Mostow’s rigidity Quasiline quasisymmetric Fuchsian group Mostow’s rigidity
分类号 O189 [理学—基础数学]
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参考文献16

  • 1Ahlfors, L. V.: Two Lectures in Kleinian Groups. In: Teichmiiller spaces and quasiconformal mappings, 1969.
  • 2Proceeding of the Romanian Finnish seminar on 60 64 Agard, S.: A geometric proof of Mostow's rigidity theorem for groups of divergence. Acta Math., 151, 231-252 (1983).
  • 3Astala, K., Zinsmeister, M.: Holomorphic families of quasi-Fuchsian groups. Ergod. Th. Dyn. Syst., 14, 207-212 (1994).
  • 4Beurling, A., Ahlfors, L. V.: The boundary correspondence under quasiconformal mappings. Acta Math., 96, 125 142 (1956).
  • 5Bishop, C. J.: Divergence groups have the Bowen property. Ann. Math., 154, 205-217 (2001).
  • 6Bowen, R.: Hausdorff dimension of quasicircles. Inst. Hautes Etudes Sci. Publ. Math., 50, 11 25 (1979).
  • 7Huo, S. J., Wu, S. J.: The failure of analyticity of Hausdorff Dimensions of quasi-circles of Fuchsian groups of second kind. Proc. Amer. Math. Soc., 143, 1101-1108 (2015).
  • 8Lehto, O.: Univalent Functions and Teichmiiller Spaces, Springer-Verlag, New York, 1987.
  • 9Lehtinen, M.: A real-analytic quasiconformal extension of a quasisymmetric function. Ann. Acad. Sci. Fenn. A I Math., 3, 207-213 (1977).
  • 10Mostow, G. D.: Quasiconformal mappings in n-space and the rigidity of hyperbolic space forms. Inst. Hautes Etudes Sci. Publ. Math., 34, 53-104 (1968).
Acta Mathematica Sinica,English Series
2016年 第4期

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