Ahlfors regular conformal dimension and Gromov–Hausdorff convergence

Nicola Cavallucci ^[1]
1. [1] École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 41, Nº 1, 2025, págs. 339-364
Idioma: inglés
DOI: 10.4171/RMI/1522
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Resumen
- 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 δ-hyperbolic metric spaces under equivariant pointed Gromov–Hausdorff convergence of the spaces.