Duality of moduli and quasiconformal mappings in metric spaces
Metric Geometry
2019-05-09 v1
Abstract
We prove a duality relation for the moduli of the family of curves connecting two sets and the family of surfaces separating the sets, in the setting of a complete metric space equipped with a doubling measure and supporting a Poincar\'e inequality. Then we apply this to show that quasiconformal mappings can be characterized by the fact that they quasi-preserve the modulus of certain families of surfaces.
Keywords
Cite
@article{arxiv.1905.02873,
title = {Duality of moduli and quasiconformal mappings in metric spaces},
author = {Rebekah Jones and Panu Lahti},
journal= {arXiv preprint arXiv:1905.02873},
year = {2019}
}