Year: 2024
Type: article
Abstract: 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.
DOI: 10.4171/rmi/1522
Author: Nicola Cavallucci
Institution: École Polytechnique Fédérale de Lausanne
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4403772916