Katrin FAESSLER
Katrin FAESSLER
Katrin FAESSLER
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Extremality of the stretch I (mean distortion)<br />
Theorem<br />
For all g ∈ F we have that<br />
<br />
K(p, fk)<br />
A(a,b)<br />
2 ρ0(p) 4 <br />
dµ(p) ≤<br />
with ρ0 = (log b<br />
Here <br />
Ω hρ4 0<br />
a )−1 ∇0 log( · H)0.<br />
dµ =<br />
Proof by modulus method.<br />
K(p, g)<br />
A(a,b)<br />
2 ρ0(p) 4 dµ(p)<br />
<br />
Ω hρ4 0 dµ<br />
<br />
Ω ρ4 0 dµ and µ denotes the Haar measure on H1 .<br />
<strong>Katrin</strong> Fässler (University of Helsinki) A stretch map on H 1<br />
HCAA 2012 15 / 23
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