0000000000049516
AUTHOR
Marshall Williams
The branch set of a quasiregular mapping between metric manifolds
Abstract In this note, we announce some new results on quantitative countable porosity of the branch set of a quasiregular mapping in very general metric spaces. As applications, we solve a recent conjecture of Fassler et al., an open problem of Heinonen–Rickman, and an open question of Heinonen–Semmes.
Distortion of quasiconformal maps in terms of the quasihyperbolic metric
Abstract We extend a theorem of Gehring and Osgood from 1979–relating to the distortion of the quasihyperbolic metric by a quasiconformal mapping between Euclidean domains–to the setting of metric measure spaces of Q -bounded geometry. When the underlying target space is bounded, we require that the boundary of the image has at least two points. We show that even in the manifold setting, this additional assumption is necessary.