Page 1

Displaying 1 – 7 of 7

Showing per page

Weak Chord-Arc Curves and Double-Dome Quasisymmetric Spheres

Vyron Vellis (2016)

Analysis and Geometry in Metric Spaces

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.

Weak slice conditions, product domains, and quasiconformal mappings.

Stephen M. Buckley, Alexander Stanoyevitch (2001)

Revista Matemática Iberoamericana

We investigate geometric conditions related to Hölder imbeddings, and show, among other things, that the only bounded Euclidean domains of the form U x V that are quasiconformally equivalent to inner uniform domains are inner uniform domains.

Currently displaying 1 – 7 of 7

Page 1