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Quantitative marked length spectrum rigidity

Karen Butt

Geometry & Topology 29 (2025) 3995–4054
Bibliography
1 W Ballmann, Lectures on spaces of nonpositive curvature, 25, Birkhäuser (1995) MR1377265
2 R Benedetti, C Petronio, Lectures on hyperbolic geometry, Springer (1992) MR1219310
3 G Besson, G Courtois, S Gallot, Entropies et rigidités des espaces localement symétriques de courbure strictement négative, Geom. Funct. Anal. 5 (1995) 731 MR1354289
4 G Besson, G Courtois, S Gallot, Minimal entropy and Mostow’s rigidity theorems, Ergodic Theory Dynam. Systems 16 (1996) 623 MR1406425
5 R Bott, L W Tu, Differential forms in algebraic topology, 82, Springer (1982) MR658304
6 M Bourdon, Structure conforme au bord et flot géodésique d’un CAT(1)-espace, Enseign. Math. 41 (1995) 63 MR1341941
7 M Bourdon, Sur le birapport au bord des CAT(1)-espaces, Inst. Hautes Études Sci. Publ. Math. 83 (1996) 95 MR1423021
8 M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
9 M Brin, H Karcher, Frame flows on manifolds with pinched negative curvature, Compos. Math. 52 (1984) 275 MR0756723
10 K H Burns, Hyperbolic behaviour of geodesic flows on manifolds with no focal points, PhD thesis, University of Warwick (1983)
11 K Burns, A Katok, Manifolds with nonpositive curvature, Ergodic Theory Dynam. Systems 5 (1985) 307 MR0796758
12 K Butt, Approximate control of the marked length spectrum by short geodesics, preprint (2022) arXiv:2210.15101
13 M P do Carmo, Riemannian geometry, Birkhäuser (1992) MR1138207
14 C Connell, B Farb, The degree theorem in higher rank, J. Differential Geom. 65 (2003) 19 MR2057530
15 D Constantine, J F Lafont, D J Thompson, The weak specification property for geodesic flows on CAT(1) spaces, Groups Geom. Dyn. 14 (2020) 297 MR4073229
16 C B Croke, Rigidity for surfaces of nonpositive curvature, Comment. Math. Helv. 65 (1990) 150 MR1036134
17 C B Croke, N S Dairbekov, Lengths and volumes in Riemannian manifolds, Duke Math. J. 125 (2004) 1 MR2097355
18 F T Farrell, L E Jones, A topological analogue of Mostow’s rigidity theorem, J. Amer. Math. Soc. 2 (1989) 257 MR973309
19 F T Farrell, P Ontaneda, The Teichmüller space of pinched negatively curved metrics on a hyperbolic manifold is not contractible, Ann. of Math. 170 (2009) 45 MR2521111
20 T Fisher, B Hasselblatt, Hyperbolic flows, Eur. Math. Soc. (2019) MR3972204
21 S Gallot, D Hulin, J Lafontaine, Riemannian geometry, Springer (1987) MR909697
22 É Ghys, P de la Harpe, editors, Sur les groupes hyperboliques d’après Mikhael Gromov, 83, Birkhäuser (1990) 1 MR1086649
23 S Gouëzel, T Lefeuvre, Classical and microlocal analysis of the x-ray transform on Anosov manifolds, Anal. PDE 14 (2021) 301 MR4229205
24 R E Greene, H Wu, Lipschitz convergence of Riemannian manifolds, Pacific J. Math. 131 (1988) 119 MR0917868
25 M Gromov, Filling Riemannian manifolds, J. Differential Geom. 18 (1983) 1 MR697984
26 M Gromov, Hyperbolic groups, from: "Essays in group theory", Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR919829
27 M Gromov, Three remarks on geodesic dynamics and fundamental group, Enseign. Math. 46 (2000) 391 MR1805410
28 C Guillarmou, G Knieper, T Lefeuvre, Geodesic stretch, pressure metric and marked length spectrum rigidity, Ergodic Theory Dynam. Systems 42 (2022) 974 MR4374964
29 C Guillarmou, T Lefeuvre, The marked length spectrum of Anosov manifolds, Ann. of Math. 190 (2019) 321 MR3990606
30 U Hamenstädt, Time-preserving conjugacies of geodesic flows, Ergodic Theory Dynam. Systems 12 (1992) 67 MR1162399
31 U Hamenstädt, Regularity at infinity of compact negatively curved manifolds, Ergodic Theory Dynam. Systems 14 (1994) 493 MR1293405
32 U Hamenstädt, Cocycles, symplectic structures and intersection, Geom. Funct. Anal. 9 (1999) 90 MR1675892
33 B Hasselblatt, Horospheric foliations and relative pinching, J. Differential Geom. 39 (1994) 57 MR1258914
34 E Heintze, H C Im Hof, Geometry of horospheres, J. Differential Geometry 12 (1977) 481 MR512919
35 S Hersonsky, F Paulin, On the rigidity of discrete isometry groups of negatively curved spaces, Comment. Math. Helv. 72 (1997) 349 MR1476054
36 M W Hirsch, C C Pugh, Smoothness of horocycle foliations, J. Differential Geom. 10 (1975) 225 MR0368077
37 V A Kaimanovich, Invariant measures of the geodesic flow and measures at infinity on negatively curved manifolds, Ann. Inst. H. Poincaré Phys. Théor. 53 (1990) 361 MR1096098
38 A Katok, B Hasselblatt, Introduction to the modern theory of dynamical systems, 54, Cambridge Univ. Press (1995) MR1326374
39 S Katok, Approximate solutions of cohomological equations associated with some Anosov flows, Ergodic Theory Dynam. Systems 10 (1990) 367 MR1062764
40 C Liverani, Decay of correlations, Ann. of Math. 142 (1995) 239 MR1343323
41 G A Margulis, Applications of ergodic theory to the investigation of manifolds of negative curvature, Funkcional. Anal. i Priložen. 3 (1969) 89 MR0257933
42 G D Mostow, Strong rigidity of locally symmetric spaces, 78, Princeton Univ. Press (1973) MR0385004
43 J P Otal, Le spectre marqué des longueurs des surfaces à courbure négative, Ann. of Math. 131 (1990) 151 MR1038361
44 J P Otal, Sur la géometrie symplectique de l’espace des géodésiques d’une variété à courbure négative, Rev. Mat. Iberoam. 8 (1992) 441 MR1202417
45 F Paulin, M Pollicott, B Schapira, Equilibrium states in negative curvature, 373, Soc. Math. France (2015) MR3444431
46 P Petersen, Riemannian geometry, 171, Springer (2006) MR2243772
47 C C Pugh, The C1,1 conclusions in Gromov’s theory, Ergodic Theory Dynam. Systems 7 (1987) 133 MR0886375
48 T Roblin, Ergodicité et équidistribution en courbure négative, 95, Soc. Math. France (2003) MR2057305
49 Y Ruan, The Cayley hyperbolic space and volume entropy rigidity, Math. Z. 306 (2024) 4 MR4670655
50 K Sigmund, On the space of invariant measures for hyperbolic flows, Amer. J. Math. 94 (1972) 31 MR0302866
51 W P Thurston, Minimal stretch maps between hyperbolic surfaces, preprint (1998) arXiv:math/9801039 MR4554454