Astala’s conjecture on distortion of Hausdorff measures under quasiconformal maps in the plane

Key words: quasiconformal mapping, Ahlfors Q-regular space, locally connected, finitely connected, m-connected, very weakly flat, property P 1 , pro- perty P 2 ∗ ,

in f*(D-l), f iswell-defined.infx(D-A),Ko-quasiconformalandnotaTeich- miiller mapping since its dilatation is not constant. In the class Q, the mapping F*of*oF is

Watanabe’s construction of X as a weak limit of branching Brownian motions, and a uniform modulus of continuity for these approximating branching systems which is

In the proof of Theorem 4, we construct a rational function which has Herman rings from those having Siegel disks, using the qc-surgery.. The same technique applies

The difference between S and the classical perimeter lies in the topology used in the definition, but both are lower semicontinuous envelopes of the usual length for regular sets..

It is in the proof of Theorem 4.1 in Section 4 that we use the abstract theories of conformal densities and Banach space-valued Sobolev mappings.. Although a direct proof could

Busemann [3] studied the top-dimensional spherical and Hausdorff meas- ures associated to a (real) Finsler metric on a differentiable manifold.. Precisely, y the

We extend to quasi- conformal mappings in the unit ball of R" a theorem of Pommcrenke concerning conformal mappings in the unit disk of the