On Dilatations and Substantial Boundary Points of Homeomorphisms of Jordan Curves

被引：0
|
作者：
Yang S. [1 ]
机构：
[1] Department of Mathematics and Computer Science, Emory University, Atlanta, 30322, GA
来源：
Results in Mathematics | 1997年 / 31卷 / 1-2期
关键词：
Affine map; Dilatation; Quasisymmetric homeomorphism; Substantial boundary point;
D O I：
10.1007/BF03322160
中图分类号：
学科分类号：
摘要：
We study the relation between the dilatations Kh and Kh* of a homeomorphism h of Jordan curves. We show that if Kh= Kh*, then either h is induced by an affine map or there is a substantial boundary point for h. In particular, we prove that if h is symmetric (in the sense of Gardiner and Sullivan), then Kh* > Kh. This is quite contrary to a previously conjectured relation between Kh and Kh*. © 1997, Birkhäuser Verlag, Basel.
引用
收藏
页码：180 / 188
页数：8
相关论文
共 50 条
  • [31] Circle homeomorphisms with two break points
    Dzhalilov, Akhtam
    Liousse, Isabelle
    NONLINEARITY, 2006, 19 (08) : 1951 - 1968
  • [32] Periodic Points of Regular Curve Homeomorphisms
    Daghar, Aymen
    Naghmouchi, Issam
    Riahi, Moncef
    QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2021, 20 (02)
  • [33] Periodic Points of Regular Curve Homeomorphisms
    Aymen Daghar
    Issam Naghmouchi
    Moncef Riahi
    Qualitative Theory of Dynamical Systems, 2021, 20
  • [34] PIERCING POINTS OF HOMEOMORPHISMS OF DIFFERENTIABLE MANIFOLDS
    PAUL, JL
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1966, 124 (03) : 518 - &
  • [35] MEASURE PRESERVING HOMEOMORPHISMS AT FIXED POINTS
    MONTGOMERY, D
    BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1945, 51 (12) : 949 - 953
  • [36] PERIODIC POINTS UNDER EXPANSIVE HOMEOMORPHISMS
    GUPTON, JR
    MATHEMATICAL SYSTEMS THEORY, 1975, 9 (02): : 105 - 108
  • [37] On μ-conformal homeomorphisms and boundary correspondence
    Gutlyanskii, Vladimir
    Sakan, Ken-ichi
    Sugawa, Toshiyuki
    COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2013, 58 (07) : 947 - 962
  • [38] SOME JORDAN CURVES AND CONVEX CURVES
    PEDERSEN, A
    AMERICAN MATHEMATICAL MONTHLY, 1988, 95 (10): : 955 - 957
  • [39] Boundary values versus dilatations of harmonic mappings
    D. Bshouty
    W. Hengartner
    Journal d’Analyse Mathematique, 1997, 72 : 141 - 164
  • [40] Boundary values versus dilatations of harmonic mappings
    Bshouty, D
    Hengartner, W
    JOURNAL D ANALYSE MATHEMATIQUE, 1997, 72 (1): : 141 - 164
12345