Katrin FAESSLER

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Definition of a Heisenberg stretch First try: gk(p)H = p k H , gk(p) := δ k−1 p (p) H BUT gk is not contact, hence not QC. <strong>Katrin</strong> Fässler (University of Helsinki) A stretch map on H 1 HCAA 2012 7 / 23
Definition of a Heisenberg stretch First try: gk(p)H = p k H , gk(p) := δ k−1 p (p) H BUT gk is not contact, hence not QC. More general does not work either. hk(p) := δ ϕk(p)(p) <strong>Katrin</strong> Fässler (University of Helsinki) A stretch map on H 1 HCAA 2012 7 / 23
Page 1 and 2: A stretch map on the Heisenberg gro
Page 3 and 4: Radial stretch maps On the complex
Page 5 and 6: The setting: Heisenberg group Defin
Page 7 and 8: Objects of study: quasiconformal ma
Page 9 and 10: Horizontal structure on the Heisenb
Page 11 and 12: Contact property of QC maps Contact
Page 13: Definition of a Heisenberg stretch
Page 17 and 18: Definition of a Heisenberg stretch
Page 19 and 20: “Logarithmic coordinates” (z, t
Page 29 and 30: Figure: “Radials” connecting tw
Page 31 and 32: Contact transformations in logarith
Page 33 and 34: Contact transformations in logarith
Page 35 and 36: Heisenberg stretch map Definition L
Page 37 and 38: Heisenberg stretch map Definition L
Page 39 and 40: Analytic characterization of QC map
Page 41 and 42: Proposition The stretch map fk, 0 <
Page 43 and 44: Extremality of the stretch I (mean
Page 45 and 46: Modulus of curve families - a ‘qu
Page 51 and 52: Choice of the curve family Γ0 Moti
Page 63 and 64: Extremality of the stretch II (maxi
Page 65 and 66:
Extremality of the stretch II (maxi
Page 67 and 68:
References A. Korányi and H. M. Re
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Katrin FAESSLER

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