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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access March 11, 2016

Weak Chord-Arc Curves and Double-Dome Quasisymmetric Spheres

  • Vyron Vellis


Let Ω be a planar Jordan domain and α > 0. We consider double-dome-like surfaces Σ(Ω, tα) over Ω where the height of the surface over any point x ∈ Ωequals dist(x, ∂Ω)α. We identify the necessary and sufficient conditions in terms of and α so that these surfaces are quasisymmetric to S2 and we show that Σ(Ω, tα) is quasisymmetric to the unit sphere S2 if and only if it is linearly locally connected and Ahlfors 2-regular.


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Received: 2015-6-5
Accepted: 2016-2-14
Published Online: 2016-3-11

© 2016 Vyron Vellis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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