Katrin FAESSLER

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Thank you for your attention! <strong>Katrin</strong> Fässler (University of Helsinki) A stretch map on H 1 HCAA 2012 21 / 23
References A. Korányi and H. M. Reimann Horizontal normal vectors and conformal capacity of spherical rings in the Heisenberg group Bull. Sci. Math. (2), 111(1):3–21, 1987 A. Korányi and H. M. Reimann Foundations for the theory of quasiconformal mappings on the Heisenberg group Adv. Math, 111(1):1–87, 1995 I. D. Platis The geometry of complex hyperbolic packs Math. Proc. Cambridge Philos. Soc., 147(1):205–234, 2009 <strong>Katrin</strong> Fässler (University of Helsinki) A stretch map on H 1 HCAA 2012 22 / 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 and 14:
Definition of a Heisenberg stretch
Page 15 and 16: 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: Extremality of the stretch II (maxi
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Katrin FAESSLER

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