Algebraic & Geometric Topology Volume 10, issue 1 (2010)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Cross curvature flow on a negatively curved solid torus

Jason DeBlois, Dan Knopf and Andrea Young

Algebraic & Geometric Topology 10 (2010) 343–372

DOI: 10.2140/agt.2010.10.343

Bibliography

1	P Acquistapace, B Terreni, Fully nonlinear parabolic systems, from: "Recent advances in nonlinear elliptic and parabolic problems (Nancy, 1988)" (editors P Bénilan, M Chipot, L C Evans, M Pierre), Pitman Res. Notes Math. Ser. 208, Longman Sci. Tech. (1989) 97 MR1035000
2	I Agol, Bounds on exceptional Dehn filling, Geom. Topol. 4 (2000) 431 MR1799796
3	I Agol, P A Storm, W P Thurston, Lower bounds on volumes of hyperbolic Haken $3$–manifolds, J. Amer. Math. Soc. 20 (2007) 1053 MR2328715
4	S Angenent, D Knopf, An example of neckpinching for Ricci flow on $S^{n+1}$, Math. Res. Lett. 11 (2004) 493 MR2092903
5	R Benedetti, C Petronio, Lectures on hyperbolic geometry, Universitext, Springer (1992) MR1219310
6	S A Bleiler, C D Hodgson, Spherical space forms and Dehn filling, Topology 35 (1996) 809 MR1396779
7	J A Buckland, Short-time existence of solutions to the cross curvature flow on $3$–manifolds, Proc. Amer. Math. Soc. 134 (2006) 1803 MR2207496
8	R D Canary, D B A Epstein, P Green, Notes on notes of Thurston, from: "Analytical and geometric aspects of hyperbolic space (Coventry/Durham, 1984)" (editor D B A Epstein), London Math. Soc. Lecture Note Ser. 111, Cambridge Univ. Press (1987) 3 MR903850
9	X Cao, Y Ni, L Saloff-Coste, Cross curvature flow on locally homogenous three-manifolds. I, Pacific J. Math. 236 (2008) 263 MR2407107
10	X Cao, L Saloff-Coste, Cross curvature flow on locally homogenous three-manifolds. II arXiv:0805.3380
11	B Chow, R S Hamilton, The cross curvature flow of $3$_-manifolds with negative sectional curvature, Turkish J. Math. 28 (2004) 1 MR2055396
12	F T Farrell, P Ontaneda, On the moduli space of negatively curved metrics of a hyperbolic manifold arXiv:0805.2635
13	F T Farrell, P Ontaneda, On the topology of the space of negatively curved metrics arXiv:math/0607367
14	F T Farrell, P Ontaneda, A caveat on the convergence of the Ricci flow for pinched negatively curved manifolds, Asian J. Math. 9 (2005) 401 MR2214959
15	D Glickenstein, Riemannian groupoids and solitons for three-dimensional homogeneous Ricci and cross-curvature flows, Int. Math. Res. Not. (2008) MR2426751
16	M Gromov, W Thurston, Pinching constants for hyperbolic manifolds, Invent. Math. 89 (1987) 1 MR892185
17	C D Hodgson, S P Kerckhoff, Rigidity of hyperbolic cone-manifolds and hyperbolic Dehn surgery, J. Differential Geom. 48 (1998) 1 MR1622600
18	C D Hodgson, S P Kerckhoff, Universal bounds for hyperbolic Dehn surgery, Ann. of Math. $(2)$ 162 (2005) 367 MR2178964
19	C D Hodgson, S P Kerckhoff, The shape of hyperbolic Dehn surgery space, Geom. Topol. 12 (2008) 1033 MR2403805
20	D Knopf, A Young, Asymptotic stability of the cross curvature flow at a hyperbolic metric, Proc. Amer. Math. Soc. 137 (2009) 699 MR2448593
21	M Lackenby, Word hyperbolic Dehn surgery, Invent. Math. 140 (2000) 243 MR1756996
22	L Ma, D Chen, Examples for cross curvature flow on $3$–manifolds, Calc. Var. Partial Differential Equations 26 (2006) 227 MR2222245
23	G A Margulis, The isometry of closed manifolds of constant negative curvature with the same fundamental group, Dokl. Akad. Nauk SSSR 192 (1970) 736 MR0266103
24	H Namazi, J Souto, Heegaard splittings and pseudo-Anosov maps, Preprint
25	G Perelman, The entropy formula for the Ricci flow and its geometric applications arXiv:math.DG/0211159
26	G Perelman, Ricci flow with surgery on three-manifolds arXiv:math.DG/0303109
27	J G Ratcliffe, Foundations of hyperbolic manifolds, Graduate Texts in Math. 149, Springer (1994) MR1299730
28	W P Thurston, The geometry and topology of three-manifolds, Princeton Univ. Math. Dept. Lecture Notes (1979)