Modulus of surface families and the radial stretch in the Heisenberg group. (English) Zbl 1375.30027
Summary: 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.
MSC:
| 30C65 | Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations |
| 30C62 | Quasiconformal mappings in the complex plane |
| 30C75 | Extremal problems for conformal and quasiconformal mappings, other methods |
| 30L10 | Quasiconformal mappings in metric spaces |
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