Geometry & Topology Volume 22, issue 5 (2018)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Rigidity for convex-cocompact actions on rank-one symmetric spaces

Guy C David and Kyle Kinneberg

Geometry & Topology 22 (2018) 2757–2790

DOI: 10.2140/gt.2018.22.2757

Bibliography

1	D Bate, Structure of measures in Lipschitz differentiability spaces, J. Amer. Math. Soc. 28 (2015) 421 MR3300699
2	D Bate, S Li, Differentiability and Poincaré-type inequalities in metric measure spaces, preprint (2015) arXiv:1505.05793
3	D Bate, S Li, Characterizations of rectifiable metric measure spaces, Ann. Sci. Éc. Norm. Supér. 50 (2017) 1 MR3621425
4	D Bate, G Speight, Differentiability, porosity and doubling in metric measure spaces, Proc. Amer. Math. Soc. 141 (2013) 971 MR3003689
5	S Bates, W B Johnson, J Lindenstrauss, D Preiss, G Schechtman, Affine approximation of Lipschitz functions and nonlinear quotients, Geom. Funct. Anal. 9 (1999) 1092 MR1736929
6	M Bonk, B Kleiner, Rigidity for quasi-Möbius group actions, J. Differential Geom. 61 (2002) 81 MR1949785
7	M Bonk, B Kleiner, Rigidity for quasi-Fuchsian actions on negatively curved spaces, Int. Math. Res. Not. 2004 (2004) 3309 MR2096259
8	M Bonk, B Kleiner, Conformal dimension and Gromov hyperbolic groups with 2–sphere boundary, Geom. Topol. 9 (2005) 219 MR2116315
9	M Bourdon, Structure conforme au bord et flot géodésique d’un CAT(−1)–espace, Enseign. Math. 41 (1995) 63 MR1341941
10	M Bourdon, Sur le birapport au bord des CAT(−1)–espaces, Inst. Hautes Études Sci. Publ. Math. 83 (1996) 95 MR1423021
11	M Bourdon, H Pajot, Poincaré inequalities and quasiconformal structure on the boundary of some hyperbolic buildings, Proc. Amer. Math. Soc. 127 (1999) 2315 MR1610912
12	R Bowen, Hausdorff dimension of quasicircles, Inst. Hautes Études Sci. Publ. Math. 50 (1979) 11 MR556580
13	M Bridgeman, R Canary, F Labourie, A Sambarino, The pressure metric for Anosov representations, Geom. Funct. Anal. 25 (2015) 1089 MR3385630
14	S V Buyalo, A M Kuznetsov, Boundary at infinity of rank-one symmetric spaces, Algebra i Analiz 21 (2009) 3 MR2604560
15	L Capogna, M Cowling, Conformality and Q–harmonicity in Carnot groups, Duke Math. J. 135 (2006) 455 MR2272973
16	J Cheeger, Differentiability of Lipschitz functions on metric measure spaces, Geom. Funct. Anal. 9 (1999) 428 MR1708448
17	J Cheeger, B Kleiner, Differentiability of Lipschitz maps from metric measure spaces to Banach spaces with the Radon–Nikodým property, Geom. Funct. Anal. 19 (2009) 1017 MR2570313
18	J Cheeger, B Kleiner, A Schioppa, Infinitesimal structure of differentiability spaces, and metric differentiation, Anal. Geom. Metr. Spaces 4 (2016) 104 MR3543676
19	R Chow, Groups quasi-isometric to complex hyperbolic space, Trans. Amer. Math. Soc. 348 (1996) 1757 MR1329530
20	C Connell, Minimal Lyapunov exponents, quasiconformal structures, and rigidity of non-positively curved manifolds, Ergodic Theory Dynam. Systems 23 (2003) 429 MR1972230
21	M Coornaert, Mesures de Patterson–Sullivan sur le bord d’un espace hyperbolique au sens de Gromov, Pacific J. Math. 159 (1993) 241 MR1214072
22	M G Cowling, A Ottazzi, Conformal maps of Carnot groups, Ann. Acad. Sci. Fenn. Math. 40 (2015) 203 MR3310079
23	G C David, Tangents and rectifiability of Ahlfors regular Lipschitz differentiability spaces, Geom. Funct. Anal. 25 (2015) 553 MR3334235
24	O Guichard, Groupes plongés quasi isométriquement dans un groupe de Lie, Math. Ann. 330 (2004) 331 MR2089430
25	U Hamenstädt, A geometric characterization of negatively curved locally symmetric spaces, J. Differential Geom. 34 (1991) 193 MR1114460
26	J Heinonen, Lectures on analysis on metric spaces, Springer (2001) MR1800917
27	J Heinonen, P Koskela, Quasiconformal maps in metric spaces with controlled geometry, Acta Math. 181 (1998) 1 MR1654771
28	J Heinonen, P Koskela, N Shanmugalingam, J T Tyson, Sobolev classes of Banach space-valued functions and quasiconformal mappings, J. Anal. Math. 85 (2001) 87 MR1869604
29	D Jerison, The Poincaré inequality for vector fields satisfying Hörmander’s condition, Duke Math. J. 53 (1986) 503 MR850547
30	W B Johnson, J Lindenstrauss, D Preiss, G Schechtman, Uniform quotient mappings of the plane, Michigan Math. J. 47 (2000) 15 MR1755254
31	I Kapovich, N Benakli, Boundaries of hyperbolic groups, from: "Combinatorial and geometric group theory" (editors S Cleary, R Gilman, A G Myasnikov, V Shpilrain), Contemp. Math. 296, Amer. Math. Soc. (2002) 39 MR1921706
32	S Keith, A differentiable structure for metric measure spaces, Adv. Math. 183 (2004) 271 MR2041901
33	S Keith, T Laakso, Conformal Assouad dimension and modulus, Geom. Funct. Anal. 14 (2004) 1278 MR2135168
34	S Keith, X Zhong, The Poincaré inequality is an open ended condition, Ann. of Math. 167 (2008) 575 MR2415381
35	K Kinneberg, Rigidity for quasi-Möbius actions on fractal metric spaces, J. Differential Geom. 100 (2015) 349 MR3343835
36	B Kleiner, J M Mackay, Differentiable structures on metric measure spaces: a primer, Ann. Sc. Norm. Super. Pisa Cl. Sci. 16 (2016) 41 MR3524664
37	A Korányi, H M Reimann, Quasiconformal mappings on the Heisenberg group, Invent. Math. 80 (1985) 309 MR788413
38	R Korte, N Marola, N Shanmugalingam, Quasiconformality, homeomorphisms between metric measure spaces preserving quasiminimizers, and uniform density property, Ark. Mat. 50 (2012) 111 MR2890347
39	E Le Donne, Metric spaces with unique tangents, Ann. Acad. Sci. Fenn. Math. 36 (2011) 683 MR2865538
40	J M Mackay, J T Tyson, Conformal dimension: theory and application, 54, Amer. Math. Soc. (2010) MR2662522
41	R Montgomery, A tour of subriemannian geometries, their geodesics and applications, 91, Amer. Math. Soc. (2002) MR1867362
42	P Pansu, Dimension conforme et sphère à l’infini des variétés à courbure négative, Ann. Acad. Sci. Fenn. Ser. A I Math. 14 (1989) 177 MR1024425
43	P Pansu, Métriques de Carnot–Carathéodory et quasiisométries des espaces symétriques de rang un, Ann. of Math. 129 (1989) 1 MR979599
44	A Schioppa, Derivations and Alberti representations, preprint (2013) arXiv:1311.2439
45	A Schioppa, Derivations and Alberti representations, Adv. Math. 293 (2016) 436 MR3474327
46	K Tan, X Yang, Subriemannian geodesics of Carnot groups of step 3, ESAIM Control Optim. Calc. Var. 19 (2013) 274 MR3023070
47	P Tukia, On quasiconformal groups, J. Analyse Math. 46 (1986) 318 MR861709
48	J Väisälä, Quasi-Möbius maps, J. Analyse Math. 44 (1984/85) 218 MR801295