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 in
Analysis and Geometry in Metric SpacesDate
2016Discipline
MatematiikkaCopyright
© 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.
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Except where otherwise noted, this item's license is described as © 2016 Vyron Vellis, published by De Gruyter Open.
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.