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Displaying similar documents to “Non-rectifiable limit sets of dimension one.”

Quasiconformal mappings of Y-pieces.

Christopher J. Bishop (2002)

Revista Matemática Iberoamericana

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In this paper we construct quasiconformal mappings between Y-pieces so that the corresponding Beltrami coefficient has exponential decay away from the boundary. These maps are used in a companion paper to construct quasiFuchsian groups whose limit sets are non-rectifiable curves of dimension 1.

A geometry on the space of probabilities (I). The finite dimensional case.

Henryk Gzyl, Lázaro Recht (2006)

Revista Matemática Iberoamericana

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In this note we provide a natural way of defining exponential coordinates on the class of probabilities on the set Ω = [1,n] or on P = {p = (p, ..., p) ∈ R| p > 0; Σ p = 1}. For that we have to regard P as a projective space and the exponential coordinates will be related to geodesic flows in C.

(n,2)-sets have full Hausdorff dimension.

Themis Mitsis (2004)

Revista Matemática Iberoamericana

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We prove that a set containing translates of every 2-plane must have full Hausdorff dimension.

Multi-parameter paraproducts.

Camil Muscalu, Jill Pipher, Terence Tao, Christoph Thiele (2006)

Revista Matemática Iberoamericana

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We prove that classical Coifman-Meyer theorem holds on any polidisc T or arbitrary dimension d ≥ 1.

Solution to the gradient problem of C.E. Weil.

Zoltán Buczolich (2005)

Revista Matemática Iberoamericana

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In this paper we give a complete answer to the famous gradient problem of C. E. Weil. On an open set G ⊂ R we construct a differentiable function f: G → R for which there exists an open set Ω ⊂ R such that ∇f(p) ∈ Ω for a p ∈ G but ∇f(q) ∉ Ω for almost every q ∈ G. This shows that the Denjoy-Clarkson property does not hold in higher dimensions.

Meromorphic functions of the form f(z) = Σ a/(z - z).

James Langley, John Rossi (2004)

Revista Matemática Iberoamericana

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We prove some results on the zeros of functions of the form f(z) = Σ a/(z - z), using quasiconformal surgery, Fourier series methods, and Baernstein's spread theorem. Our results have applications to fixpoints of entire functions.