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Displaying similar documents to “On the pointwise dimension of hyperbolic measures: a proof of the Eckmann-Ruelle conjecture.”

Boundaries of right-angled hyperbolic buildings

Jan Dymara, Damian Osajda (2007)

Fundamenta Mathematicae

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We prove that the boundary of a right-angled hyperbolic building is a universal Menger space. As a consequence, the 3-dimensional universal Menger space is the boundary of some Gromov-hyperbolic group.

On the Hausdorff dimension of piecewise hyperbolic attractors

Tomas Persson (2010)

Fundamenta Mathematicae

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We study non-invertible piecewise hyperbolic maps in the plane. The Hausdorff dimension of the attractor is calculated in terms of the Lyapunov exponents, provided that the map satisfies a transversality condition. Explicit examples of maps for which this condition holds are given.

Tameness on the boundary and Ahlfors' measure conjecture

Jeffrey Brock, Kenneth Bromberg, Richard Evans, Juan Souto (2003)

Publications Mathématiques de l'IHÉS

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Let N be a complete hyperbolic 3-manifold that is an algebraic limit of geometrically finite hyperbolic 3-manifolds. We show N is homeomorphic to the interior of a compact 3-manifold, or , if one of the following conditions holds: 1. N has non-empty conformal boundary, 2. N is not homotopy equivalent to a compression body, or 3. N is a strong limit of geometrically finite manifolds. The first case proves Ahlfors’ measure conjecture for kleinian groups in the closure of the geometrically...

Regenerating hyperbolic cone 3-manifolds from dimension 2

Joan Porti (2013)

Annales de l’institut Fourier

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We prove that a closed 3-orbifold that fibers over a hyperbolic polygonal 2-orbifold admits a family of hyperbolic cone structures that are viewed as regenerations of the polygon, provided that the perimeter is minimal.