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A Sufficient Condition for Rigidity in Extremality of Teichmller Equivalence Classes by Schwarzian Derivative

A Sufficient Condition for Rigidity in Extremality of Teichmller Equivalence Classes by Schwarzian Derivative
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摘要 The Strebel point is a TeichmOller equivalence class in the Teichmuller space that has a certain rigidity in the extremality of the maximal dilatation. In this paper, we give a sufficient condition in terms of the Schwarzian derivative for a Teichmuller equivalence class of the universal Teichmuller space under which the class is a Strebel point. As an application, we construct a Teichmuller equivalence class that is a Strebel point and that is not an asymptotically conformal class. The Strebel point is a TeichmOller equivalence class in the Teichmuller space that has a certain rigidity in the extremality of the maximal dilatation. In this paper, we give a sufficient condition in terms of the Schwarzian derivative for a Teichmuller equivalence class of the universal Teichmuller space under which the class is a Strebel point. As an application, we construct a Teichmuller equivalence class that is a Strebel point and that is not an asymptotically conformal class.
作者 Masahiro Yanagishita
机构地区 Departments in Fundamental Science and Engineering
出处 《Analysis in Theory and Applications》 2014年第1期130-135,共6页 分析理论与应用（英文刊）
关键词 Strebel points the Schwarzian derivative asymptotically conformal maps. Strebel points, the Schwarzian derivative, asymptotically conformal maps.
分类号 O186.12 [理学—基础数学]
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参考文献7

  • 1C. J. Earle, F. P. Gardiner and N. Lakic, Asymptotic Teichmuller space, part I: the complex structure, Contemp. Math., 256 (2000), 17-38.
  • 2C. J. Earle, F. P. Gardiner and N. Lakic, Asymptotic Teichmuller space, part II: the metric structure, Contemp. Math., 355 (2004), 187-219.
  • 3C. J. Earle, V. Markovic and D. Saric, Barycentric extension and the Bers embedding for asymptotic Teichmuller space, Contemp. Math., 311 (2002),87-105.
  • 4C. J. Earle and Zhong Li, Isometrically embedded polydisks in infinite dimensional Teichmuller spaces, J. Geom. Anal., 9 (1999),51-71.
  • 5F. P. Gardiner and N. Lakic, Quasiconformal Teichmuller theory, Amer. Math. SoC., 2000.
  • 6N. Lakic, Strebel points, Contemp. Math., 211 (1997),417-431, Amer. Math. SoC., 1997.
  • 7O. Lehto, Univalent Functions and Teichmuller Spaces, Graduate Texts in Mathmatics Vol. 109, Springer-Verlag, New York, 1987.
Analysis in Theory and Applications
2014年 第1期

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