Modulus of surface families and the radial stretch in the Heisenberg group

17 Oct 2015 · Platis Ioannis D. ·

We develop a modulus method for surface families inside a domain in the Heisenberg group and we prove that the stretch map between two Heisenberg spherical rings is a minimiser for the mean distortion among the class of contact quasiconformal maps between these rings which satisfy certain boundary conditions.