Katrin FAESSLER

Heisenberg stretch map
Definition
Let 0 < k < 1. The Heisenberg stretch map is given by
Properties:
fk(ξ, ψ, η) = (kξ, tan −1 tan ψ
( k ), η).
fk is quasiconformal with fk(p)H = p k H ,
fk preserves C × {0}, moreover fk(z, 0) = (z|z| k−1 , 0),
z
f−1(z, t) = |z| 2 −t , −it |z| 4 +t2
is 1-QC inversion in the Korányi unit
sphere with inversion relations
dH(f−1(p), f−1(q)) = dH(p, q)
pHqH
Katrin Fässler (University of Helsinki) A stretch map on H 1
and f−1(p)H = 1
.
pH
HCAA 2012 12 / 23