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Variation of quasiconformal mappings on lines

Leonid V. Kovalev, Jani Onninen (2009)

Studia Mathematica

We obtain improved regularity of homeomorphic solutions of the reduced Beltrami equation, as compared to the standard Beltrami equation. Such an improvement is not possible in terms of Hölder or Sobolev regularity; instead, our results concern the generalized variation of restrictions to lines. Specifically, we prove that the restriction to any line segment has finite p-variation for all p > 1 but not necessarily for p = 1.

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 181 – 200 of 245