Weak Chord-Arc Curves and Double-Dome Quasisymmetric Spheres

Vyron 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 -