Dimensions of limit sets of Kleinian groups

被引:1
|
作者
Falk, Kurt [1 ]
机构
[1] Christian Albrechts Univ Kiel, Math Seminar, Ludewig Meyn Str 4, D-24118 Kiel, Germany
关键词
NORMAL-SUBGROUPS; HAUSDORFF DIMENSION; CRITICAL EXPONENTS; AMENABILITY; GROWTH; SPECTRUM; CONVERGENCE; ENTROPY; BOTTOM;
D O I
10.1090/conm/731/14674
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper we give a brief survey of results on dimension gaps for limit sets of geometrically infinite Kleinian groups. We concentrate on an important notion from geometric group theory, amenability, as a criterion for the existence of such gaps.
引用
收藏
页码:95 / 114
页数:20
相关论文
共 50 条
  • [1] WILD KNOTS IN HIGHER DIMENSIONS AS LIMIT SETS OF KLEINIAN GROUPS
    Boege, Margareta
    Hinojosa, Gabriela
    Verjovsky, Alberto
    [J]. CONFORMAL GEOMETRY AND DYNAMICS, 2009, 13 : 197 - 216
  • [2] Remarks on Hausdorff dimensions for transient limit sets of Kleinian groups
    Falk, K
    Stratmann, BO
    [J]. TOHOKU MATHEMATICAL JOURNAL, 2004, 56 (04) : 571 - 582
  • [3] FRACTAL DIMENSIONS OF LIMIT-SETS OF SOME KLEINIAN-GROUPS
    FRAME, M
    HEFFERON, J
    [J]. LECTURE NOTES IN MATHEMATICS, 1990, 1440 : 74 - 80
  • [4] LIMIT SETS AND COMMENSURABILITY OF KLEINIAN GROUPS
    Yang, Wen-Yuan
    Jiang, Yue-Ping
    [J]. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2010, 82 (01) : 1 - 9
  • [5] RESIDUAL LIMIT SETS OF KLEINIAN GROUPS
    ABIKOFF, W
    [J]. ACTA MATHEMATICA, 1973, 130 (1-2) : 127 - 144
  • [6] On horospheric limit sets of Kleinian groups
    Falk, Kurt
    Matsuzaki, Katsuhiko
    [J]. JOURNAL OF FRACTAL GEOMETRY, 2020, 7 (04) : 329 - 350
  • [7] KLEINIAN GROUPS WITH UNBOUNDED LIMIT SETS
    BEARDON, AF
    [J]. GLASGOW MATHEMATICAL JOURNAL, 1972, 13 (MAR) : 24 - &
  • [8] The Poincare Exponent and the Dimensions of Kleinian Limit Sets
    Fraser, Jonathan M.
    [J]. AMERICAN MATHEMATICAL MONTHLY, 2022, 129 (05): : 480 - 484
  • [9] Wild knots as limit sets of kleinian groups
    Hinojosa, G
    [J]. GEOMETRY AND DYNAMICS, 2005, 389 : 125 - 139
  • [10] Limit sets of cyclic quaternionic Kleinian groups
    Dutta, Sandipan
    Gongopadhyay, Krishnendu
    Lohan, Tejbir
    [J]. GEOMETRIAE DEDICATA, 2023, 217 (04)