Geodesic
Weak Chord-Arc Curves and Double-Dome Quasisymmetric Spheres
Analysis and Geometry in Metric Spaces, Tome 4 (2016) no. 1 Cet article a éte moissonné depuis la source The Polish Digital Mathematics Library

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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.
Mots-clés : quasisymmetric spheres, double-dome-like surfaces, chord-arc property, Ahlfors 2-regularity 
@article{AGMS_2016_4_1_a6,
     author = {Vellis, Vyron},
     title = {Weak {Chord-Arc} {Curves} and {Double-Dome} {Quasisymmetric} {Spheres}},
     journal = {Analysis and Geometry in Metric Spaces},
     year = {2016},
     volume = {4},
     number = {1},
     zbl = {1336.30035},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AGMS_2016_4_1_a6/}
}
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Vellis, Vyron. Weak Chord-Arc Curves and Double-Dome Quasisymmetric Spheres. Analysis and Geometry in Metric Spaces, Tome 4 (2016) no. 1. http://geodesic.mathdoc.fr/item/AGMS_2016_4_1_a6/