Volume 22, issue 3 (2018)

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

Volume 27
Issue 6, 2049–2496
Issue 5, 1657–2048
Issue 4, 1273–1655
Issue 3, 823–1272
Issue 2, 417–821
Issue 1, 1–415

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 Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Ricci flow on asymptotically Euclidean manifolds

Yu Li

Geometry & Topology 22 (2018) 1837–1891
Bibliography
1 R A Adams, J J F Fournier, Sobolev spaces, 140, Elsevier (2003) MR2424078
2 R Arnowitt, S Deser, C W Misner, Coordinate invariance and energy expressions in general relativity, Phys. Rev. 122 (1961) 997 MR0127946
3 T Aubin, Some nonlinear problems in Riemannian geometry, Springer (1998) MR1636569
4 S Axler, P Bourdon, W Ramey, Harmonic function theory, 137, Springer (1992) MR1184139
5 S Bando, A Kasue, H Nakajima, On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth, Invent. Math. 97 (1989) 313 MR1001844
6 R Bartnik, The mass of an asymptotically flat manifold, Comm. Pure Appl. Math. 39 (1986) 661 MR849427
7 L Bessières, G Besson, S Maillot, Ricci flow on open 3–manifolds and positive scalar curvature, Geom. Topol. 15 (2011) 927 MR2821567
8 X Cao, Q S Zhang, The conjugate heat equation and ancient solutions of the Ricci flow, Adv. Math. 228 (2011) 2891 MR2838064
9 A Chau, L F Tam, C Yu, Pseudolocality for the Ricci flow and applications, Canad. J. Math. 63 (2011) 55 MR2779131
10 B L Chen, Strong uniqueness of the Ricci flow, J. Differential Geom. 82 (2009) 363 MR2520796
11 B Chow, S C Chu, D Glickenstein, C Guenther, J Isenberg, T Ivey, D Knopf, P Lu, F Luo, L Ni, The Ricci flow : techniques and applications, II : Analytic aspects, 144, Amer. Math. Soc. (2008) MR2365237
12 B Chow, S C Chu, D Glickenstein, C Guenther, J Isenberg, T Ivey, D Knopf, P Lu, F Luo, L Ni, The Ricci flow : techniques and applications, III : Geometric-analytic aspects, 163, Amer. Math. Soc. (2010) MR2604955
13 B Chow, P Lu, L Ni, Hamilton’s Ricci flow, 77, Amer. Math. Soc. (2006) MR2274812
14 B Chow, P Lu, B Yang, Lower bounds for the scalar curvatures of noncompact gradient Ricci solitons, C. R. Math. Acad. Sci. Paris 349 (2011) 1265 MR2861997
15 T H Colding, W P Minicozzi II, Width and finite extinction time of Ricci flow, Geom. Topol. 12 (2008) 2537 MR2460871
16 X Dai, L Ma, Mass under the Ricci flow, Comm. Math. Phys. 274 (2007) 65 MR2318848
17 M Feldman, T Ilmanen, D Knopf, Rotationally symmetric shrinking and expanding gradient Kähler–Ricci solitons, J. Differential Geom. 65 (2003) 169 MR2058261
18 D Gilbarg, N S Trudinger, Elliptic partial differential equations of second order, 224, Springer (1983) MR737190
19 L Gross, Logarithmic Sobolev inequalities, Amer. J. Math. 97 (1975) 1061 MR0420249
20 R S Hamilton, The formation of singularities in the Ricci flow, from: "Surveys in differential geometry, II" (editor S T Yau), International Press (1995) 7 MR1375255
21 R Haslhofer, A mass-decreasing flow in dimension three, Math. Res. Lett. 19 (2012) 927 MR3008425
22 H J Hein, C LeBrun, Mass in Kähler geometry, Comm. Math. Phys. 347 (2016) 183 MR3543182
23 G Huisken, T Ilmanen, The inverse mean curvature flow and the Riemannian Penrose inequality, J. Differential Geom. 59 (2001) 353 MR1916951
24 B Kleiner, J Lott, Notes on Perelman’s papers, Geom. Topol. 12 (2008) 2587 MR2460872
25 B Kleiner, J Lott, Singular Ricci flows, I, preprint (2014) arXiv:1408.2271
26 J M Lee, T H Parker, The Yamabe problem, Bull. Amer. Math. Soc. 17 (1987) 37 MR888880
27 P Li, S T Yau, On the parabolic kernel of the Schrödinger operator, Acta Math. 156 (1986) 153 MR834612
28 D McFeron, G Székelyhidi, On the positive mass theorem for manifolds with corners, Comm. Math. Phys. 313 (2012) 425 MR2942956
29 J Morgan, G Tian, Ricci flow and the Poincaré conjecture, 3, Amer. Math. Soc. (2007) MR2334563
30 O Munteanu, J Wang, Smooth metric measure spaces with non-negative curvature, Comm. Anal. Geom. 19 (2011) 451 MR2843238
31 G Perelman, The entropy formula for the Ricci flow and its geometric applications, preprint (2002) arXiv:math/0211159
32 G Perelman, Finite extinction time for the solutions to the Ricci flow on certain three-manifolds, preprint (2003) arXiv:math/0307245v1
33 G Perelman, Ricci flow with surgery on three-manifolds, preprint (2003) arXiv:math.DG/0303109
34 O S Rothaus, Logarithmic Sobolev inequalities and the spectrum of Schrödinger operators, J. Funct. Anal. 42 (1981) 110 MR620582
35 R M Schoen, Variational theory for the total scalar curvature functional for Riemannian metrics and related topics, from: "Topics in calculus of variations" (editor M Giaquinta), Lecture Notes in Math. 1365, Springer (1989) 120 MR994021
36 R Schoen, S T Yau, On the proof of the positive mass conjecture in general relativity, Comm. Math. Phys. 65 (1979) 45 MR526976
37 R Schoen, S T Yau, On the structure of manifolds with positive scalar curvature, Manuscripta Math. 28 (1979) 159 MR535700
38 R Schoen, S T Yau, Lectures on differential geometry, International Press (1994) MR1333601
39 N Sesum, G Tian, X Wang, Notes on Perelman’s paper on the entropy formula for the Ricci flow and its geometric applications, preprint (2004)
40 W X Shi, Ricci deformation of the metric on complete noncompact Riemannian manifolds, J. Differential Geom. 30 (1989) 303 MR1010165
41 G Tian, J Viaclovsky, Bach-flat asymptotically locally Euclidean metrics, Invent. Math. 160 (2005) 357 MR2138071
42 P Topping, Lectures on the Ricci flow, 325, Cambridge Univ. (2006) MR2265040
43 E Witten, A new proof of the positive energy theorem, Comm. Math. Phys. 80 (1981) 381 MR626707
44 Q S Zhang, Strong noncollapsing and uniform Sobolev inequalities for Ricci flow with surgeries, Pacific J. Math. 239 (2009) 179 MR2449017
45 Q S Zhang, Extremal of log Sobolev inequality and W entropy on noncompact manifolds, J. Funct. Anal. 263 (2012) 2051 MR2956934