Some conditions for quasiconformality

Sufficient conditions for quasiconformality of harmonic mappings of the upper halfplane onto itself

In this paper we introduce a class of increasing homeomorphic self-mappings of R. We define a harmonic extension of such functions to the upper halfplane by means of the Poisson integral. Our main results give some sufficient conditions for quasiconformality of the extension.

Doubling Measures, Monotonicity, and Quasiconformality

We construct quasiconformal mappings in Euclidean spaces by integration of a discontinuous kernel against doubling measures with suitable decay. The differentials of mappings that arise in this way satisfy an isotropic form of the doubling condition. We prove that this isotropic doubling condition is satisfied by the distance functions of certain fractal sets. Finally, we construct an isotropic...

Quasiconformality, Quasisymmetry, and Removability in Loewner Spaces

where L(x,r) := sup{|f (x)−f (y)| : |x−y| ≤ r}, l(x,r) := inf {|f (x)−f (y)| : |x−y| ≥ r}, and by |x− y| we denote the distance between x and y in a metric space. We say that f is quasiconformal if there is a constant H so that H(x)≤H for every x ∈X. This infinitesimal condition is easy to state but not easy to use. For instance, it is not clear from the definition if the inverse mapping is qua...

Some Sufficient Conditions for Univalence

A new subclass R(u), 0 < u < I, of the class St(I/2) the class of starlike functions of order I/2 is introduced and it is shown that R(u) is closed with respect to the Hadamard product of analytic functions. Some sufficient conditions for the normalized regular functions to be univalent in the unit disk E are given.

Some Results on Necessary Conditions for Tow Quasidifferentiable Optimization Problems