Quasiconformal extension of quasisymmetric mappings compatible with a Möbius group
نویسندگان
چکیده
منابع مشابه
Quasiconformal Extension of Harmonic Mappings in the Plane
Let f be a sense-preserving harmonic mapping in the unit disk. We give a sufficient condition in terms of the pre-Schwarzian derivative of f to ensure that it can be extended to a quasiconformal map in the complex plane. Introduction A well-known criterion due to Becker [5] states that if a locally univalent analytic function φ in the unit disk D satisfies (1) sup z∈D ∣∣∣∣φ′′(z) φ′(z) ∣∣∣∣ (1− ...
متن کاملQuasi-isometric Extensions of Quasisymmetric Mappings of the Real Line Compatible with Composition
We show that it is possible to extend, in a homomorphic fashion, each quasisymmetric homeomorphism of the real line to a quasi-isometry of the upper-half plane. Epstein and Markovic have recently shown that a homomorphic extension to quasiconformal homeomorphisms of the upper-half plane is not possible.
متن کاملQuasiconformal Mappings in Space
U' denotes the image of U, the disk | s — So| and maps the infinitesimal circles | z — zo\ = e onto infinitesimal ellipses; H(z0) gives the ratio of the major to minor axes and J(zo) is the absolute value of the Jacobian. Suppose next that w(z) is continuously difîerentiable with J(z)>...
متن کاملQuasiconformal Geometry of Monotone Mappings
This paper concerns a class of monotone mappings in a Hilbert space that can be viewed as a nonlinear version of the class of positive invertible operators. Such mappings are proved to be open, locally Hölder continuous, and quasisymmetric. They arise naturally from the Beurling-Ahlfors extension and from Brenier’s polar factorization, and find applications in the geometry of metric spaces and ...
متن کاملQuasiconformal Mappings Which Increase Dimension
For any compact set E ⊂ R , d ≥ 1 , with Hausdorff dimension 0 < dim(E) < d and for any ε > 0 , there is a quasiconformal mapping (quasisymmetric if d = 1) f of R to itself such that dim(f(E)) > d− ε .
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Mathematica
سال: 1985
ISSN: 0001-5962
DOI: 10.1007/bf02392471