Volume 17, issue 1 (2013)

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The deformation theory of hyperbolic cone–$3$–manifolds with cone-angles less than $2\pi$

Hartmut Weiß

Geometry & Topology 17 (2013) 329–367
Bibliography
1 M Boileau, B Leeb, J Porti, Geometrization of 3–dimensional orbifolds, Ann. of Math. 162 (2005) 195 MR2178962
2 J Brüning, M Lesch, Hilbert complexes, J. Funct. Anal. 108 (1992) 88 MR1174159
3 J Brüning, R Seeley, An index theorem for first order regular singular operators, Amer. J. Math. 110 (1988) 659 MR955293
4 A Casson, An example of weak non-rigidity for cone manifolds with vertices, Talk at the third MSJ regional workshop, Tokyo (1998)
5 J Cheeger, On the Hodge theory of Riemannian pseudomanifolds, from: "Geometry of the Laplace operator (Proc. Sympos. Pure Math., Univ. Hawaii, Honolulu, Hawaii, 1979)", Proc. Sympos. Pure Math. XXXVI, Amer. Math. Soc. (1980) 91 MR573430
6 J Cheeger, Spectral geometry of singular Riemannian spaces, J. Differential Geom. 18 (1983) 575 MR730920
7 D Cooper, C D Hodgson, S P Kerckhoff, Three-dimensional orbifolds and cone-manifolds, 5, Mathematical Society of Japan (2000) MR1778789
8 J B Gil, G A Mendoza, Adjoints of elliptic cone operators, Amer. J. Math. 125 (2003) 357 MR1963689
9 C D Hodgson, S P Kerckhoff, Rigidity of hyperbolic cone-manifolds and hyperbolic Dehn surgery, J. Differential Geom. 48 (1998) 1 MR1622600
10 M Kapovich, Hyperbolic manifolds and discrete groups, 183, Birkhäuser (2001) MR1792613
11 M Lesch, Operators of Fuchs type, conical singularities, and asymptotic methods, 136, B. G. Teubner Verlagsgesellschaft mbH (1997) 190 MR1449639
12 F Luo, G Tian, Liouville equation and spherical convex polytopes, Proc. Amer. Math. Soc. 116 (1992) 1119 MR1137227
13 Y Matsushima, S Murakami, On vector bundle valued harmonic forms and automorphic forms on symmetric riemannian manifolds, Ann. of Math. 78 (1963) 365 MR0153028
14 R Mazzeo, Elliptic theory of differential edge operators I, Comm. Partial Differential Equations 16 (1991) 1615 MR1133743
15 R Mazzeo, G Montcouquiol, Infinitesimal rigidity of cone-manifolds and the Stoker problem for hyperbolic and Euclidean polyhedra, J. Differential Geom. 87 (2011) 525 MR2819548
16 R Mazzeo, H Weiss, Teichmüller theory for conic surfaces, in preparation
17 R B Melrose, The Atiyah–Patodi–Singer index theorem, 4, A K Peters Ltd. (1993) MR1348401
18 R B Melrose, G Mendoza, Elliptic operators of totally characteristic type, MSRI preprint (1983)
19 G Montcouquiol, Deformations of hyperbolic convex polyhedra and cone-3-manifolds, Geom. Dedicata (to appear)
20 G Montcouquiol, H Weiss, Complex twist flows on surface group representations and the local shape of the deformation space of hyperbolic cone-3–manifolds, Geom. Topol. 17 (2013) 369
21 J Porti, H Weiss, Deforming Euclidean cone 3–manifolds, Geom. Topol. 11 (2007) 1507 MR2326950
22 B W Schulze, Pseudo-differential operators on manifolds with singularities, 24, North-Holland Publishing Co. (1991) MR1142574
23 M Troyanov, Prescribing curvature on compact surfaces with conical singularities, Trans. Amer. Math. Soc. 324 (1991) 793 MR1005085
24 H Weiss, Local rigidity of 3–dimensional cone-manifolds, J. Differential Geom. 71 (2005) 437 MR2198808