The Assouad spectrum of Kleinian limit sets and Patterson-Sullivan measure

Jonathan Fraser, Liam Stuart*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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.
Original languageEnglish
Article number1
Number of pages32
JournalGeometriae Dedicata
Publication statusPublished - 10 Oct 2022


  • Kleinian group
  • Limit set
  • Patterson-Sullivan measure
  • Parabolic points
  • Assouad dimension
  • Assouad spectrum


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