Geometry & Topology Volume 23, issue 4 (2019)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Hausdorff dimension of boundaries of relatively hyperbolic groups

Leonid Potyagailo and Wen-yuan Yang

Geometry & Topology 23 (2019) 1779–1840

DOI: 10.2140/gt.2019.23.1779

Bibliography

1	C J Bishop, P W Jones, Hausdorff dimension and Kleinian groups, Acta Math. 179 (1997) 1 MR1484767
2	B H Bowditch, Relatively hyperbolic groups, Internat. J. Algebra Comput. 22 (2012) MR2922380
3	M Burger, S Mozes, CAT(−1)–spaces, divergence groups and their commensurators, J. Amer. Math. Soc. 9 (1996) 57 MR1325797
4	J W Cannon, The combinatorial structure of cocompact discrete hyperbolic groups, Geom. Dedicata 16 (1984) 123 MR758901
5	M Coornaert, Mesures de Patterson–Sullivan sur le bord d’un espace hyperbolique au sens de Gromov, Pacific J. Math. 159 (1993) 241 MR1214072
6	M Coornaert, T Delzant, A Papadopoulos, Géométrie et théorie des groupes : les groupes hyperboliques de Gromov, 1441, Springer (1990) MR1075994
7	F Dal’Bo, M Peigné, J C Picaud, A Sambusetti, On the growth of quotients of Kleinian groups, Ergodic Theory Dynam. Systems 31 (2011) 835 MR2794950
8	C Druţu, M Sapir, Tree-graded spaces and asymptotic cones of groups, Topology 44 (2005) 959 MR2153979
9	K Falconer, Fractal geometry: mathematical foundations and applications, Wiley (1990) MR1102677
10	W J Floyd, Group completions and limit sets of Kleinian groups, Invent. Math. 57 (1980) 205 MR568933
11	D Gaboriau, F Paulin, Sur les immeubles hyperboliques, Geom. Dedicata 88 (2001) 153 MR1877215
12	V Gerasimov, Expansive convergence groups are relatively hyperbolic, Geom. Funct. Anal. 19 (2009) 137 MR2507221
13	V Gerasimov, Floyd maps for relatively hyperbolic groups, Geom. Funct. Anal. 22 (2012) 1361 MR2989436
14	V Gerasimov, L Potyagailo, Quasi-isometric maps and Floyd boundaries of relatively hyperbolic groups, J. Eur. Math. Soc. 15 (2013) 2115 MR3120738
15	V Gerasimov, L Potyagailo, Non-finitely generated relatively hyperbolic groups and Floyd quasiconvexity, Groups Geom. Dyn. 9 (2015) 369 MR3356972
16	V Gerasimov, L Potyagailo, Quasiconvexity in relatively hyperbolic groups, J. Reine Angew. Math. 710 (2016) 95 MR3437561
17	V Gerasimov, L Potyagailo, Similar relatively hyperbolic actions of a group, Int. Math. Res. Not. 2016 (2016) 2068 MR3509947
18	É Ghys, P de la Harpe, Sur les groupes hyperboliques d’après Mikhael Gromov, 83, Birkhäuser (1990) MR1086650
19	M Gromov, Hyperbolic groups, from: "Essays in group theory" (editor S Gersten), Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR919829
20	J Heinonen, Lectures on analysis on metric spaces, Springer (2001) MR1800917
21	G C Hruska, Relative hyperbolicity and relative quasiconvexity for countable groups, Algebr. Geom. Topol. 10 (2010) 1807 MR2684983
22	A Karlsson, Free subgroups of groups with nontrivial Floyd boundary, Comm. Algebra 31 (2003) 5361 MR2005231
23	J M Mackay, A Sisto, Quasi-hyperbolic planes in relatively hyperbolic groups, preprint (2012) arXiv:1111.2499v2
24	P Mattila, Geometry of sets and measures in Euclidean spaces : fractals and rectifiability, 44, Cambridge Univ. Press (1995) MR1333890
25	S J Patterson, The limit set of a Fuchsian group, Acta Math. 136 (1976) 241 MR0450547
26	F Paulin, On the critical exponent of a discrete group of hyperbolic isometries, Differential Geom. Appl. 7 (1997) 231 MR1480536
27	M J Puls, The first L^p–cohomology of some groups with one end, Arch. Math. (Basel) 88 (2007) 500 MR2325882
28	A Sisto, On metric relative hyperbolicity, preprint (2012) arXiv:1210.8081
29	B O Stratmann, The exponent of convergence of Kleinian groups : on a theorem of Bishop and Jones, from: "Fractal geometry and stochastics, III" (editors C Bandt, U Mosco, M Zähle), Progr. Probab. 57, Birkhäuser (2004) 93 MR2087134
30	B Stratmann, M Urbański, The box-counting dimension for geometrically finite Kleinian groups, Fund. Math. 149 (1996) 83 MR1372359
31	B Stratmann, S L Velani, The Patterson measure for geometrically finite groups with parabolic elements, new and old, Proc. London Math. Soc. 71 (1995) 197 MR1327939
32	D Sullivan, The density at infinity of a discrete group of hyperbolic motions, Inst. Hautes Études Sci. Publ. Math. 50 (1979) 171 MR556586
33	D Sullivan, Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups, Acta Math. 153 (1984) 259 MR766265
34	P Tukia, Conical limit points and uniform convergence groups, J. Reine Angew. Math. 501 (1998) 71 MR1637829
35	W Woess, Random walks on infinite graphs and groups, 138, Cambridge Univ. Press (2000) MR1743100
36	W Y Yang, Patterson–Sullivan measures and growth of relatively hyperbolic groups, preprint (2013) arXiv:1308.6326
37	W Y Yang, Growth tightness for groups with contracting elements, Math. Proc. Cambridge Philos. Soc. 157 (2014) 297 MR3254594
38	W Y Yang, Peripheral structures of relatively hyperbolic groups, J. Reine Angew. Math. 689 (2014) 101 MR3187929