Displaying similar documents to “Quasiconformal dimensions of self-similar fractals.”

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.

Quasiconformal groups of compact type.

Petra Bonfert-Taylor, Gaven Martin (2005)

Revista Matemática Iberoamericana

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We establish that a quasiconformal group is of compact type if and only if its limits set is purely conical and find that the limit set of a quasiconformal group of compact type is uniformly perfect. A key tool is the result of Bowditch-Tukia on compact-type convergence groups. These results provide crucial tools for studying the deformations of quasiconformal groups and in establishing isomorphisms between such groups and conformal groups.

Non-rectifiable limit sets of dimension one.

Christopher J. Bishop (2002)

Revista Matemática Iberoamericana

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We construct quasiconformal deformations of convergence type Fuchsian groups such that the resulting limit set is a Jordan curve of Hausdorff dimension 1, but having tangents almost nowhere. It is known that no divergence type group has such a deformation. The main tools in this construction are (1) a characterization of tangent points in terms of Peter Jones' beta's, (2) a result of Stephen Semmes that gives a Carleson type condition on a Beltrami coefficient which implies rectifiability...

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.

Periodic quasiregular mappings of finite order.

David Drasin, Swati Sastry (2003)

Revista Matemática Iberoamericana

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The authors construct a periodic quasiregular function of any finite order p, 1 < p < infinity. This completes earlier work of O. Martio and U. Srebro.

Mappings of finite distortion: sharp Orlicz-conditions.

Janne Kauhanen, Pekka Koskela, Jan Malý, Jani Onninen, Xiao Zhong (2003)

Revista Matemática Iberoamericana

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We establish continuity, openness and discreteness, and the condition (N) for mappings of finite distortion under minimal integrability assumptions on the distortion.

(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.