65 citations · 398 across the 74 of their papers we have counts for
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Hausdorff measure of quasicircles
István Prause, Xavier Tolsa, Ignacio Uriarte-Tuero
S. Smirnov proved recently that the Hausdorff dimension of any K-quasicircle is at most 1+k^2, where k=(K-1)/(K+1). In this paper we show that if is such a quasicircle, then $H…
Quasiconformal distortion of Hausdorff measures
Xavier Tolsa
In this paper we prove that if f is a planar K-quasiconformal map and 0<t<2, t' = 2t/(2K-Kt+t), then f transforms sets of finite (t')-Hausdorff measure into sets of finite t-Hausdo…
Quasiconformal maps, analytic capacity, and non linear potentials
Xavier Tolsa, Ignacio Uriarte-Tuero
In this paper we prove that if $ϕ:\C\to\C$ is a -quasiconformal map, with , and $E\subset \C$ is a compact set contained in a ball , then $$\frac{\dot C_{\frac{2K}{2K+1}…
A dual characterization of the C^1 harmonic capacity and applications
Albert Mas, Mark Melnikov, Xavier Tolsa
The Lipschitz and C^1 harmonic capacities K and K_c in R^n can be considered as high-dimensional versions of the so-called analytic and continuous analytic capacities G and A (resp…