Volume 12, issue 5 (2008)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 28
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
Other MSP Journals
Notes on Perelman's papers

Bruce Kleiner and John Lott

Geometry & Topology 12 (2008) 2587–2855
1 K Akutagawa, M Ishida, C LeBrun, Perelman's invariant, Ricci flow, and the Yamabe invariants of smooth manifolds, Arch. Math. $($Basel$)$ 88 (2007) 71 MR2289603
2 G Anderson, B Chow, A pinching estimate for solutions of the linearized Ricci flow system on 3-manifolds, Calc. Var. Partial Differential Equations 23 (2005) 1 MR2133658
3 M T Anderson, Scalar curvature and geometrization conjectures for $3$-manifolds, from: "Comparison geometry (Berkeley, CA, 1993–94)", Math. Sci. Res. Inst. Publ. 30, Cambridge Univ. Press (1997) 49 MR1452867
4 M T Anderson, Scalar curvature and the existence of geometric structures on 3-manifolds. I, J. Reine Angew. Math. 553 (2002) 125 MR1944810
5 M T Anderson, Canonical metrics on 3-manifolds and 4-manifolds, Asian J. Math. 10 (2006) 127 MR2213687
6 S B Angenent, D Knopf, Precise asymptotics of the Ricci flow neckpinch, Comm. Anal. Geom. 15 (2007) 773 MR2395258
7 W Ballmann, M Gromov, V Schroeder, Manifolds of nonpositive curvature, Progress in Mathematics 61, Birkhäuser (1985) MR823981
8 W Beckner, Geometric asymptotics and the logarithmic Sobolev inequality, Forum Math. 11 (1999) 105 MR1673903
9 L Bessières, G Besson, M Boileau, S Maillot, J Porti, Weak Collapsing and Geometrisation of Aspherical 3-Manifolds arXiv:0706.2065
10 J P Bourguignon, Une stratification de l'espace des structures riemanniennes, Compositio Math. 30 (1975) 1 MR0418147
11 D Burago, Y Burago, S Ivanov, A course in metric geometry, Graduate Studies in Mathematics 33, Amer. Math. Soc. (2001) MR1835418
12 Y Burago, M Gromov, G Perelman, A. D. Aleksandrov spaces with curvatures bounded below, Uspekhi Mat. Nauk 47 (1992) 3, 222 MR1185284
13 E Calabi, An extension of E. Hopf's maximum principle with an application to Riemannian geometry, Duke Math. J. 25 (1958) 45 MR0092069
14 H D Cao, B Chow, Recent developments on the Ricci flow, Bull. Amer. Math. Soc. $($N.S.$)$ 36 (1999) 59 MR1655479
15 H D Cao, X P Zhu, A complete proof of the Poincaré and geometrization conjectures—application of the Hamilton-Perelman theory of the Ricci flow, Asian J. Math. 10 (2006) 165 MR2233789
16 I Chavel, Riemannian geometry—a modern introduction, Cambridge Tracts in Mathematics 108, Cambridge University Press (1993) MR1271141
17 J Cheeger, D G Ebin, Comparison theorems in Riemannian geometry, North-Holland Mathematical Library 9, North-Holland Publishing Co. (1975) MR0458335
18 J Cheeger, D Gromoll, On the structure of complete manifolds of nonnegative curvature, Ann. of Math. $(2)$ 96 (1972) 413 MR0309010
19 J Cheeger, M Gromov, M Taylor, Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds, J. Differential Geom. 17 (1982) 15 MR658471
20 B L Chen, X P Zhu, Uniqueness of the Ricci flow on complete noncompact manifolds, J. Differential Geom. 74 (2006) 119 MR2260930
21 B Chow, D Knopf, The Ricci flow: an introduction, Mathematical Surveys and Monographs 110, Amer. Math. Soc. (2004) MR2061425
22 B Chow, P Lu, L Ni, Hamilton's Ricci flow, Graduate Studies in Mathematics 77, Amer. Math. Soc. (2006) MR2274812
23 T H Colding, W P Minicozzi II, Estimates for the extinction time for the Ricci flow on certain 3-manifolds and a question of Perelman, J. Amer. Math. Soc. 18 (2005) 561 MR2138137
24 T H Colding, W P Minicozzi II, Width and Finite Extinction Time of Ricci Flow, Geom. Topol. 12 (2008) 2537
25 J Dodziuk, Maximum principle for parabolic inequalities and the heat flow on open manifolds, Indiana Univ. Math. J. 32 (1983) 703 MR711862
26 J H Eschenburg, Local convexity and nonnegative curvature—Gromov's proof of the sphere theorem, Invent. Math. 84 (1986) 507 MR837525
27 R S Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982) 255 MR664497
28 R S Hamilton, The Ricci flow on surfaces, from: "Mathematics and general relativity (Santa Cruz, CA, 1986)", Contemp. Math. 71, Amer. Math. Soc. (1988) 237 MR954419
29 R S Hamilton, A compactness property for solutions of the Ricci flow, Amer. J. Math. 117 (1995) 545 MR1333936
30 R S Hamilton, The formation of singularities in the Ricci flow, from: "Surveys in differential geometry, Vol. II (Cambridge, MA, 1993)", Int. Press, Cambridge, MA (1995) 7 MR1375255
31 R S Hamilton, Four-manifolds with positive isotropic curvature, Comm. Anal. Geom. 5 (1997) 1 MR1456308
32 R S Hamilton, Non-singular solutions of the Ricci flow on three-manifolds, Comm. Anal. Geom. 7 (1999) 695 MR1714939
33 H Ishii, On the equivalence of two notions of weak solutions, viscosity solutions and distribution solutions, Funkcial. Ekvac. 38 (1995) 101 MR1341739
34 V Kapovitch, Perelman's Stability Theorem, from: "Surveys in differential geometry, Vol. XI (Metric and Comparison Geometry)", Int. Press, Cambridge, MA (2007) 103
35 B Kleiner, J Lott, Locally Collapsed $3$-Manifolds, to appear
36 B Kleiner, J Lott, Notes and commentary on Perelman's Ricci flow papers
37 P Lu, G Tian, Uniqueness of standard solutions in the work of Perelman
38 S Matveev, Algorithmic topology and classification of 3-manifolds, Algorithms and Computation in Mathematics 9, Springer (2003) MR1997069
39 W H Meeks III, S T Yau, Topology of three-dimensional manifolds and the embedding problems in minimal surface theory, Ann. of Math. $(2)$ 112 (1980) 441 MR595203
40 J W Morgan, Recent progress on the Poincaré conjecture and the classification of 3-manifolds, Bull. Amer. Math. Soc. $($N.S.$)$ 42 (2005) 57 MR2115067
41 J Morgan, G Tian, Completion of Perelman's proof of the geometrization conjecture arXiv:0809.4040
42 J Morgan, G Tian, Ricci flow and the Poincaré conjecture, Clay Mathematics Monographs 3, Amer. Math. Soc. (2007) MR2334563
43 G D Mostow, Strong rigidity of locally symmetric spaces, Princeton University Press (1973) MR0385004
44 L Ni, The entropy formula for linear heat equation, J. Geom. Anal. 14 (2004) 87 MR2030576
45 L Ni, A note on Perelman's LYH-type inequality, Comm. Anal. Geom. 14 (2006) 883 MR2287149
46 G Perelman, The entropy formula for the Ricci flow and its geometric applications arXiv:math.DG/0211159
47 G Perelman, Ricci flow with surgery on three-manifolds arXiv:math.DG/0303109
48 G Perelman, Finite extinction time for the solutions to the Ricci flow on certain three-manifolds arXiv:math.DG/0307245
49 G Prasad, Strong rigidity of $\mathbf{Q}$-rank $1$ lattices, Invent. Math. 21 (1973) 255 MR0385005
50 M Reed, B Simon, Methods of modern mathematical physics. IV. Analysis of operators, Academic Press (1978) MR0493421
51 O S Rothaus, Logarithmic Sobolev inequalities and the spectrum of Schrödinger operators, J. Funct. Anal. 42 (1981) 110 MR620582
52 R Schoen, Estimates for stable minimal surfaces in three-dimensional manifolds, from: "Seminar on minimal submanifolds", Ann. of Math. Stud. 103, Princeton Univ. Press (1983) 111 MR795231
53 R Schoen, S T Yau, Complete three-dimensional manifolds with positive Ricci curvature and scalar curvature, from: "Seminar on Differential Geometry", Ann. of Math. Stud. 102, Princeton Univ. Press (1982) 209 MR645740
54 P Scott, The geometries of $3$-manifolds, Bull. London Math. Soc. 15 (1983) 401 MR705527
55 V Sharafutdinov, The Pogorelov–Klingenberg theorem for manifolds that are homeomorphic to $\mathbb{R}^n$, Siberian Math. J. 18 (1977) 649
56 W X Shi, Deforming the metric on complete Riemannian manifolds, J. Differential Geom. 30 (1989) 223 MR1001277
57 W X Shi, Ricci deformation of the metric on complete noncompact Riemannian manifolds, J. Differential Geom. 30 (1989) 303 MR1010165
58 T Shioya, T Yamaguchi, Volume collapsed three-manifolds with a lower curvature bound, Math. Ann. 333 (2005) 131 MR2169831
59 W P Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. $($N.S.$)$ 6 (1982) 357 MR648524
60 P Topping, Lectures on the Ricci flow, London Mathematical Society Lecture Note Series 325, Cambridge University Press (2006) MR2265040
61 R Ye, On the Uniqueness of 2-Dimensional $\kappa$-Solutions
62 R Ye, On the $l$-function and the reduced volume of Perelman. I, Trans. Amer. Math. Soc. 360 (2008) 507 MR2342013