Weak Chord-Arc Curves and Double-Dome Quasisymmetric Spheres
Vellis, V. (2016). Weak Chord-Arc Curves and Double-Dome Quasisymmetric Spheres. Analysis and Geometry in Metric Spaces, 4 (1). doi:10.1515/agms-2016-0002
Published inAnalysis and Geometry in Metric Spaces
© 2016 Vyron Vellis, published by De Gruyter Open. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.
Let Ω be a planar Jordan domain and α > 0. We consider double-dome-like surfaces Σ(Ω, t α ) over Ω where the height of the surface over any point x ∈ Ω equals dist(x, ∂Ω) α . We identify the necessary and su cient conditions in terms of Ω and α so that these surfaces are quasisymmetric to S 2 and we show that Σ(Ω, t α ) is quasisymmetric to the unit sphere S 2 if and only if it is linearly locally connected and Ahlfors 2-regular.