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Duality of Moduli and Quasiconformal Mappings in Metric Spaces
- Source :
- Analysis and Geometry in Metric Spaces, Vol 8, Iss 1, Pp 166-181 (2020)
- Publication Year :
- 2020
- Publisher :
- De Gruyter, 2020.
-
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 Poincaré 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.
Details
- Language :
- English
- ISSN :
- 22993274
- Volume :
- 8
- Issue :
- 1
- Database :
- Directory of Open Access Journals
- Journal :
- Analysis and Geometry in Metric Spaces
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.124632cb86cf460b9fcb9dfcf8cdc5db
- Document Type :
- article
- Full Text :
- https://doi.org/10.1515/agms-2020-0112