Weak Chord-Arc Curves and Double-Dome Quasisymmetric Spheres

• Autorzy: Vyron Vellis
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2016
• Tom: 4
• Numer: 1

Daty

otrzymano

2015-06-05

zaakceptowano

2016-02-14

online

2016-03-11

Twórcy

autor

Vyron Vellis

• Department of Mathematics and Statistics, P.O. Box 35 (MaD), FI-40014 University of Jyväskylä, Jyväskylä, Finland

Identyfikatory

DOI

10.1515/agms-2016-0002