Geometry & Topology Volume 22, issue 3 (2018)

Download this article
	For screen
	For printing

Recent Issues

The Journal

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

DOI: 10.2140/gt.2018.22.1837

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