On quasiconformal non-equivalence of gasket Julia sets and limit sets

Abstract

This paper studies quasiconformal non-equivalence of Julia sets and limit sets. We proved that any Julia set is quasiconformally different from the Apollonian gasket. We also proved that any Julia set of a quadratic rational map is quasiconformally different from the gasket limit set of a geometrically finite Kleinian group.

25 pages without references, 7 figures. v2: minor changes

References in corpus (3)

• Circle packings, kissing reflection groups and critically fixed anti-rational maps
• On Deformation Space Analogies between Kleinian Reflection Groups and Antiholomorphic Rational Maps
• Circle packings, renormalizations and subdivision rules