# Weak Chord-Arc Curves and Double-Dome Quasisymmetric Spheres

Analysis and Geometry in Metric Spaces (2016)

- Volume: 4, Issue: 1, page 54-67, electronic only
- ISSN: 2299-3274

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topVyron Vellis. "Weak Chord-Arc Curves and Double-Dome Quasisymmetric Spheres." Analysis and Geometry in Metric Spaces 4.1 (2016): 54-67, electronic only. <http://eudml.org/doc/276690>.

@article{VyronVellis2016,

abstract = {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.},

author = {Vyron Vellis},

journal = {Analysis and Geometry in Metric Spaces},

keywords = {quasisymmetric spheres; double-dome-like surfaces; chord-arc property; Ahlfors 2-regularity},

language = {eng},

number = {1},

pages = {54-67, electronic only},

title = {Weak Chord-Arc Curves and Double-Dome Quasisymmetric Spheres},

url = {http://eudml.org/doc/276690},

volume = {4},

year = {2016},

}

TY - JOUR

AU - Vyron Vellis

TI - Weak Chord-Arc Curves and Double-Dome Quasisymmetric Spheres

JO - Analysis and Geometry in Metric Spaces

PY - 2016

VL - 4

IS - 1

SP - 54

EP - 67, electronic only

AB - 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.

LA - eng

KW - quasisymmetric spheres; double-dome-like surfaces; chord-arc property; Ahlfors 2-regularity

UR - http://eudml.org/doc/276690

ER -

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