Geometry & Topology Volume 27, issue 1 (2023)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

Rotational symmetry of ancient solutions to the Ricci flow in higher dimensions

Simon Brendle and Keaton Naff

Geometry & Topology 27 (2023) 153–226

DOI: 10.2140/gt.2023.27.153

Bibliography

1	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
2	S Angenent, S Brendle, P Daskalopoulos, N Šešum, Unique asymptotics of compact ancient solutions to three-dimensional Ricci flow, Comm. Pure Appl. Math. 75 (2022) 1032 MR4400906
3	S Angenent, P Daskalopoulos, N Sesum, Unique asymptotics of ancient convex mean curvature flow solutions, J. Differential Geom. 111 (2019) 381 MR3934596
4	S Angenent, P Daskalopoulos, N Sesum, Uniqueness of two-convex closed ancient solutions to the mean curvature flow, Ann. of Math. 192 (2020) 353 MR4151080
5	N Berline, E Getzler, M Vergne, Heat kernels and Dirac operators, Springer (2004) MR2273508
6	S Brendle, A general convergence result for the Ricci flow in higher dimensions, Duke Math. J. 145 (2008) 585 MR2462114
7	S Brendle, A generalization of Hamilton’s differential Harnack inequality for the Ricci flow, J. Differential Geom. 82 (2009) 207 MR2504774
8	S Brendle, Ricci flow and the sphere theorem, 111, Amer. Math. Soc. (2010) MR2583938
9	S Brendle, Rotational symmetry of self-similar solutions to the Ricci flow, Invent. Math. 194 (2013) 731 MR3127066
10	S Brendle, Rotational symmetry of Ricci solitons in higher dimensions, J. Differential Geom. 97 (2014) 191 MR3231974
11	S Brendle, Ricci flow with surgery in higher dimensions, Ann. of Math. 187 (2018) 263 MR3739233
12	S Brendle, Ricci flow with surgery on manifolds with positive isotropic curvature, Ann. of Math. 190 (2019) 465 MR3997128
13	S Brendle, Ancient solutions to the Ricci flow in dimension 3, Acta Math. 225 (2020) 1 MR4176064
14	S Brendle, K Choi, Uniqueness of convex ancient solutions to mean curvature flow in ℝ³, Invent. Math. 217 (2019) 35 MR3958790
15	S Brendle, K Choi, Uniqueness of convex ancient solutions to mean curvature flow in higher dimensions, Geom. Topol. 25 (2021) 2195 MR4310889
16	S Brendle, P Daskalopoulos, N Sesum, Uniqueness of compact ancient solutions to three-dimensional Ricci flow, Invent. Math. 226 (2021) 579 MR4323639
17	S Brendle, G Huisken, C Sinestrari, Ancient solutions to the Ricci flow with pinched curvature, Duke Math. J. 158 (2011) 537 MR2805067
18	B L Chen, X P Zhu, Ricci flow with surgery on four-manifolds with positive isotropic curvature, J. Differential Geom. 74 (2006) 177 MR2258799
19	B Chow, P Lu, L Ni, Hamilton’s Ricci flow, 77, Amer. Math. Soc. (2006) MR2274812
20	R S Hamilton, Eternal solutions to the Ricci flow, J. Differential Geom. 38 (1993) 1 MR1231700
21	R S Hamilton, The Harnack estimate for the Ricci flow, J. Differential Geom. 37 (1993) 225 MR1198607
22	R S Hamilton, The formation of singularities in the Ricci flow, from: "Surveys in differential geometry, II" (editor S T Yau), International (1995) 7 MR1375255
23	R S Hamilton, Four-manifolds with positive isotropic curvature, Comm. Anal. Geom. 5 (1997) 1 MR1456308
24	R Haslhofer, O Hershkovits, Ancient solutions of the mean curvature flow, Comm. Anal. Geom. 24 (2016) 593 MR3521319
25	B Kleiner, J Lott, Singular Ricci flows, I, Acta Math. 219 (2017) 65 MR3765659
26	X Li, L Ni, K Wang, Four-dimensional gradient shrinking solitons with positive isotropic curvature, Int. Math. Res. Not. 2018 (2018) 949 MR3801452
27	X Li, Y Zhang, Ancient solutions to the Ricci flow in higher dimensions, preprint (2018) arXiv:1812.04156
28	M J Micallef, J D Moore, Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two-planes, Ann. of Math. 127 (1988) 199 MR924677
29	O Munteanu, J Wang, Positively curved shrinking Ricci solitons are compact, J. Differential Geom. 106 (2017) 499 MR3680555
30	K Naff, Shrinking Ricci solitons with positive isotropic curvature, preprint (2019) arXiv:1905.10305
31	G Perelman, The entropy formula for the Ricci flow and its geometric applications, preprint (2002) arXiv:math/0211159
32	G Perelman, Ricci flow with surgery on three-manifolds, preprint (2003) arXiv:math/0303109
33	B White, The nature of singularities in mean curvature flow of mean-convex sets, J. Amer. Math. Soc. 16 (2003) 123 MR1937202