紧线体上拟共形映射Teichmüller等价类的一个刻画
A Description of the Teichmüller Equivalent Quasi-Conformal Mapping Class on the Compact Solenoid
DOI: 10.12677/PM.2018.81007, PDF,    国家自然科学基金支持
作者: 宋 飞*：北京航空航天大学数学与系统科学学院，北京
关键词: 紧线体；Teichmüller空间；拟共形映射；万有覆盖；Compact Solenoid； Teichmüller Space； Quasi-Conformal Mapping； Universal Covering
摘要: 本文讨论了紧线体 的Teichmüller空间在标记紧线体意义下的表示，并且给出了两个拟共形映射 Teichmüller等价在其万有覆盖的极限集中的一个刻画，我们证明了两个拟共形映射具有相同的极限集映射值当且仅当它们是Teichmüller等价的。
Abstract: Let be the compact solenoid. In the present article, we give a representation of the Teichmúller space of in the sense of being marked. Moreover, we give the description of the Teichmüller equivalence of quasi-conformal maps in the universal covering space of . We prove that two quasi-conformal maps have common value in the limit set if and only if they are Teichmüller equivalent.
文章引用：宋飞. 紧线体上拟共形映射Teichmüller等价类的一个刻画[J]. 理论数学, 2018, 8(1): 41-46. https://doi.org/10.12677/PM.2018.81007

参考文献

[1] Sullivan, D. (1993) Linking the Universallities of Milnor-Thurston. Feigenbaum and Ahlfors-Bers. In: Goldberg, L. and Phillips, A., Eds., Topological Methods in Modern Mathematics, Publish or Perish, Houston, 543-563.
[2] Ehrenpreis, L. (1970) Cohomology with Bounds. Symposia Mathematics IV (INDAM, Rome, 1968/69), Academic Press, London, 389-395.
[3] Saric, D. (2008) On Quasiconformal Deformations of the Universal Hyperbolic Solenoid. Journal d’Analyse Mathematique, 105, 303-343. [Google Scholar] [CrossRef] 
[4] Odden, C. (2005) The Baseleaf Preserving Mapping Class Group of the Uni-versal Hyperbolic Solenoid. Tran. American Mathematical Society, 357, 1829-1858. [Google Scholar] [CrossRef] 
[5] Saric, D. (2007) Earthquakes and Thurston Boundary for the Teichmüller Space of the Universal Hyperbolic Solenoid. Pacific Journal of Mathematics, 233, 205-228. [Google Scholar] [CrossRef] 
[6] Penner, R.C. and Saric, D. (2008) Teichmüller Theory of the Punctured Solenoid. Geometriae Dedicata, 132, 179-212. [Google Scholar] [CrossRef] 
[7] Sullivan, D. (1992) Bounds Quadratic Differentials and Renormalization Con-jectures. American Mathematical Society Centennial Publications, Vol. II, Amer. Math. Soc., Providence.
[8] Imayoshi, Y. and Taniguchi, M. (1992) An Introduction to Teichmüller spaces. Springer-Varlag, Tokyo, Berlin, Heidelberg, New York.
[9] MacLane, S. (1998) Categories for the Working Mathematician. 2nd Edition, Springer.

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