Wall properties of domains in euclidean spaces.
Weak Chord-Arc Curves and Double-Dome Quasisymmetric Spheres
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.
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.
Weighted Sobolev and Poincaré Inequalities and Quasiregular Mappings of Polynomial Type.
Whitney covers and quasi-isometry of -averaging domains.
Whitney-type theorems on extension of functions on Carnot groups.
Wiman and Arima theorems for quasiregular mappings.