6533b853fe1ef96bd12abf3d
RESEARCH PRODUCT
Quasihyperbolic boundary conditions and capacity: Hölder continuity of quasiconformal mappings
Pekka KoskelaJani OnninenJeremy T. Tysonsubject
Quasiconformal mappingUniform continuityMathematics::Complex VariablesGeneral MathematicsMathematical analysisMetric (mathematics)Mathematics::Metric GeometryHölder conditionBoundary value problemDomain (mathematical analysis)Modulus of continuityMathematicsdescription
We prove that quasiconformal maps onto domains which satisfy a suitable growth condition on the quasihyperbolic metric are uniformly continuous when the source domain is equipped with the internal metric. The obtained modulus of continuity and the growth assumption on the quasihyperbolic metric are shown to be essentially sharp. As a tool, we prove a new capacity estimate.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2001-09-01 | Commentarii Mathematici Helvetici |