We show that if Ω ⊂ Rn+1, n ≥ 1, is a uniform domain (aka 1sided NTA domain), i.e., a domain which enjoys interior Corkscrew and Harnack Chain conditions, then uniform rectifiability of the boundary… (More)

The high prevalence of eating disorders in Arab countries indicates a need for an Arabic language screening tool. This study aimed to validate an Arabic version (A-SCOFF) of the British SCOFF… (More)

In the present paper we prove that for any open connected set Ω ⊂ R, n ≥ 1, and any E ⊂ ∂Ω with H(E) < ∞, absolute continuity of the harmonic measure ω with respect to the Hausdorff measure on E… (More)

We assume that Ω1,Ω2 ⊂ R, n ≥ 1 are two disjoint domains whose complements satisfy a uniform thickness condition and the intersection of their boundaries F has positive harmonic measure. Then we show… (More)

A theorem of David and Jerison asserts that harmonic measure is absolutely continuous with respect to surface measure in NTA domains with Ahlfors regular boundaries. We prove that this fails in high… (More)

On the Sierpinski Gasket (SG) and related fractals, we define a notion of conformal energy Eφ and conformal Laplacian ∆φ for a given conformal factor φ, based on the corresponding notions in… (More)

Here we describe Tyson’s theorem on the equivalence of geometric quasiconformality, local-quasisymmetry, and a variant of metric quasiconformality on domains of metric spaces and give a summary of… (More)

A quasiplane f(V ) is the image of an n-dimensional Euclidean subspace V of R (1 ≤ n ≤ N − 1) under a quasiconformal map f : R → R . We give sufficient conditions in terms of the weak quasisymmetry… (More)

We prove that there exists M > 0 such that for any closed rectifiable curve Γ in Hilbert space, almost every point in Γ is contained in a countable union of M chord-arc curves whose total length is… (More)