Definitions for a Class of Plane Quasiconformal Mappings
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− ...
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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)>...
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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 ...
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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 .
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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 1967
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000024272