TY - JOUR
T1 - An explicit counterexample to the equivariant K = 2 conjecture
AU - Komori, Yohei
AU - Matthews, Charles A.
PY - 2006/8/24
Y1 - 2006/8/24
N2 - We construct an explicit example of a geometrically finite Kleinian group G with invariant component Ω in the Riemann sphere Ĉ such that any quasiconformal map from Ω to the boundary of the convex hull of Ĉ − Ω in H3 which extends to the identity map on their common boundary in Ĉ, and which is equivariant under the group of Möbius transformations preserving Ω, must have maximal dilatation K 2.002.
AB - We construct an explicit example of a geometrically finite Kleinian group G with invariant component Ω in the Riemann sphere Ĉ such that any quasiconformal map from Ω to the boundary of the convex hull of Ĉ − Ω in H3 which extends to the identity map on their common boundary in Ĉ, and which is equivariant under the group of Möbius transformations preserving Ω, must have maximal dilatation K 2.002.
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U2 - 10.1090/S1088-4173-06-00153-6
DO - 10.1090/S1088-4173-06-00153-6
M3 - Article
AN - SCOPUS:54149106849
SN - 1088-4173
VL - 10
SP - 184
EP - 196
JO - Conformal Geometry and Dynamics
JF - Conformal Geometry and Dynamics
IS - 10
ER -