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Ahlfors regular conformal dimension and Gromov–Hausdorff convergence
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We prove that the Ahlfors regular conformal dimension is upper semicontinuous with respect to Gromov–Hausdorff convergence when restricted to the class of uniformly perfect, uniformly quasi-selfsimilar metric spaces. Moreover, we show the continuity of the Ahlfors regular conformal dimension in case of limit sets of discrete, quasiconvex-cocompact group of isometries of uniformly bounded codiameter of
\delta
-hyperbolic metric spaces under equivariant pointed Gromov–Hausdorff convergence of the spaces.
European Mathematical Society - EMS - Publishing House GmbH
Title: Ahlfors regular conformal dimension and Gromov–Hausdorff convergence
Description:
We prove that the Ahlfors regular conformal dimension is upper semicontinuous with respect to Gromov–Hausdorff convergence when restricted to the class of uniformly perfect, uniformly quasi-selfsimilar metric spaces.
Moreover, we show the continuity of the Ahlfors regular conformal dimension in case of limit sets of discrete, quasiconvex-cocompact group of isometries of uniformly bounded codiameter of
\delta
-hyperbolic metric spaces under equivariant pointed Gromov–Hausdorff convergence of the spaces.
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