The Assouad spectrum of Kleinian limit sets and Patterson-Sullivan measure
Abstract
The Assouad dimension of the limit set of a geometrically finite Kleinian group with parabolics may exceed the Hausdorff and box dimensions. The Assouad spectrum is a continuously parametrised family of dimensions which ‘interpolates’ between the box and Assouad dimensions of a fractal set. It is designed to reveal more subtle geometric information than the box and Assouad dimensions considered in isolation. We conduct a detailed analysis of the Assouad spectrum of limit sets of geometrically finite Kleinian groups and the associated Patterson-Sullivan measure. Our analysis reveals several novel features, such as interplay between horoballs of different rank not seen the box or Assouad dimensions.
Citation
Fraser , J & Stuart , L 2022 , ' The Assouad spectrum of Kleinian limit sets and Patterson-Sullivan measure ' , Geometriae Dedicata , vol. 217 , 1 . https://doi.org/10.1007/s10711-022-00734-2
Publication
Geometriae Dedicata
Status
Peer reviewed
ISSN
0046-5755Type
Journal article
Rights
Copyright © The Author(s) 2022. Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Description
Funding information: JMF was financially supported by an EPSRC Standard Grant (EP/R015104/1) and a Leverhulme Trust Research Project Grant (RPG-2019-034). LS was financially supported by the University of St Andrews.Collections
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