Old and new on the quasihyperbolic metric. (English) Zbl 0888.30019
Duren, Peter (ed.) et al., Quasiconformal mappings and analysis. A collection of papers honoring Frederick W. Gehring to his 70th birthday. Proceedings of the international symposium, Ann Arbor, MI, USA, August 1995. New York, NY: Springer. 205-219 (1998).
This article is a nicely written general survey discussing the quasihyperbolic metric from its first appearance unto recent developments; over fifty papers are referenced. Topics covered include the relation between the quasihyperbolic metric and the geometry of domains, connections between the growth of the quasihyperbolic metric and dimension estimates of the boundary, applications to quasiconformal maps and conformal capacity, the role of the quasihyperbolic metric in Poincaré inequalities and applications to partial differential equations.
For the entire collection see [Zbl 0883.00018].
For the entire collection see [Zbl 0883.00018].
Reviewer: S.Staples (Fort Worth)
MSC:
| 30C65 | Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations |
| 30D50 | Blaschke products, etc. (MSC2000) |
| 35J60 | Nonlinear elliptic equations |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 26A16 | Lipschitz (Hölder) classes |
