Limit sets and convex cocompact groups in higher rank symmetric spaces
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- by Sungwoon Kim
- Proc. Amer. Math. Soc. 147 (2019), 361-368
- DOI: https://doi.org/10.1090/proc/14228
- Published electronically: August 10, 2018
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Abstract:
We show that every limit point of a Zariski dense discrete subgroup $\Gamma$ of the isometry group of a symmetric space of noncompact type is conical if and only if $\Gamma$ is convex cocompact.References
- P. Albuquerque, Patterson-Sullivan theory in higher rank symmetric spaces, Geom. Funct. Anal. 9 (1999), no. 1, 1–28. MR 1675889, DOI 10.1007/s000390050079
- Yves Benoist, Automorphismes des cônes convexes, Invent. Math. 141 (2000), no. 1, 149–193 (French, with English and French summaries). MR 1767272, DOI 10.1007/PL00005789
- B. H. Bowditch, Geometrical finiteness with variable negative curvature, Duke Math. J. 77 (1995), no. 1, 229–274. MR 1317633, DOI 10.1215/S0012-7094-95-07709-6
- B. H. Bowditch, Relatively hyperbolic groups, Internat. J. Algebra Comput. 22 (2012), no. 3, 1250016, 66. MR 2922380, DOI 10.1142/S0218196712500166
- Patrick B. Eberlein, Geometry of nonpositively curved manifolds, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1996. MR 1441541
- Bruce Kleiner and Bernhard Leeb, Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings, Inst. Hautes Études Sci. Publ. Math. 86 (1997), 115–197 (1998). MR 1608566
- Bruce Kleiner and Bernhard Leeb, Rigidity of invariant convex sets in symmetric spaces, Invent. Math. 163 (2006), no. 3, 657–676. MR 2207236, DOI 10.1007/s00222-005-0471-y
- G. Link, Hausdorff dimension of limit sets of discrete subgroups of higher rank Lie groups, Geom. Funct. Anal. 14 (2004), no. 2, 400–432. MR 2062761, DOI 10.1007/s00039-004-0462-y
- Gabriele Link, Geometry and dynamics of discrete isometry groups of higher rank symmetric spaces, Geom. Dedicata 122 (2006), 51–75. MR 2295541, DOI 10.1007/s10711-006-9090-z
- Gabriele Link, Ergodicity of generalised Patterson-Sullivan measures in higher rank symmetric spaces, Math. Z. 254 (2006), no. 3, 611–625. MR 2244369, DOI 10.1007/s00209-006-0962-6
- A. Parreau, Dégénérescences de sous-groupes discrets de groupes de Lie semisimples et actions de groupes sur des immeubles affines, Thèse de doctorat, Orsay (2000).
- J.-F. Quint, Groupes convexes cocompacts en rang supérieur, Geom. Dedicata 113 (2005), 1–19 (French, with English summary). MR 2171296, DOI 10.1007/s10711-005-0122-x
Bibliographic Information
- Sungwoon Kim
- Affiliation: Department of Mathematics, Jeju National University, 102 Jejudaehak-ro, Jeju, 63243, Republic of Korea
- MR Author ID: 982647
- Email: sungwoon@jejunu.ac.kr
- Received by editor(s): January 11, 2018
- Received by editor(s) in revised form: April 30, 2018
- Published electronically: August 10, 2018
- Additional Notes: This work was supported by a research grant of Jeju National University in 2017.
- Communicated by: Kenneth Bromberg
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 361-368
- MSC (2010): Primary 53C35, 22E40
- DOI: https://doi.org/10.1090/proc/14228
- MathSciNet review: 3876755