The Apollonian inner metric and uniform domains
โ Scribed by M. Huang; S. Ponnusamy; X. Wang; S. K. Sahoo
- Book ID
- 102493013
- Publisher
- John Wiley and Sons
- Year
- 2010
- Tongue
- English
- Weight
- 152 KB
- Volume
- 283
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
โฆ Synopsis
In this paper we characterize uniform domains in terms of the Apollonian inner metric and the j-metric, thus providing solutions to two open problems given in [16]. We also discuss the relationships among uniform, A-uniform, Apollonian quasiconvex and quasi-isotropic domains.
๐ SIMILAR VOLUMES
In this paper, we first introduce L~(tt)-averaging domains which are generalizations of existing domains, such as John domains and LS(#)-averaging domains. Then, we characterize L~ (#)-averaging domains using the quasihyperbolic metric. Finally, we give applications to quasiconformal mappings.