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On the classification of gradient Ricci solitons

Peter Petersen and William Wylie

Geometry & Topology 14 (2010) 2277–2300
Bibliography
1 P Baird, L Danielo, Three-dimensional Ricci solitons which project to surfaces, J. Reine Angew. Math. 608 (2007) 65 MR2339469
2 A L Besse, Einstein manifolds, 10, Springer (1987) MR867684
3 C Böhm, B Wilking, Nonnegatively curved manifolds with finite fundamental groups admit metrics with positive Ricci curvature, Geom. Funct. Anal. 17 (2007) 665 MR2346271
4 C Böhm, B Wilking, Manifolds with positive curvature operators are space forms, Ann. of Math. (2) 167 (2008) 1079 MR2415394
5 H W Brinkmann, Einstein spaces which are mapped conformally on each other, Math. Ann. 94 (1925) 119 MR1512246
6 E Calabi, An extension of E Hopf’s maximum principle with an application to Riemannian geometry, Duke Math. J. 25 (1958) 45 MR0092069
7 H D Cao, Recent progress on Ricci solitons, from: "Recent advances in geometric analysis" (editors Y I Lee, C S Lin, M P Tsui), Adv. Lect. Math. 11, Int. Press (2010) 1 MR2648937
8 X Cao, Compact gradient shrinking Ricci solitons with positive curvature operator, J. Geom. Anal. 17 (2007) 425 MR2358764
9 X Cao, B Wang, Z Zhang, On locally conformally flat gradient shrinking Ricci solitons arXiv:0807.0588v3
10 G Catino, C Mantegazza, Evolution of the Weyl tensor under the Ricci flow arXiv:0910.4761v4
11 J Cheeger, T H Colding, Lower bounds on Ricci curvature and the almost rigidity of warped products, Ann. of Math. (2) 144 (1996) 189 MR1405949
12 H Chen, Pointwise 1 4–pinched 4-manifolds, Ann. Global Anal. Geom. 9 (1991) 161 MR1136125
13 X Chen, P Lu, G Tian, A note on uniformization of Riemann surfaces by Ricci flow, Proc. Amer. Math. Soc. 134 (2006) 3391 MR2231924
14 B Chow, D Knopf, The Ricci flow : an introduction, 110, Amer. Math. Soc. (2004) MR2061425
15 B Chow, P Lu, L Ni, Hamilton’s Ricci flow, 77, Amer. Math. Soc. (2006) MR2274812
16 M Eminenti, G La Nave, C Mantegazza, Ricci solitons: the equation point of view, Manuscripta Math. 127 (2008) 345 MR2448435
17 R E Greene, H Wu, C approximations of convex, subharmonic, and plurisubharmonic functions, Ann. Sci. École Norm. Sup. (4) 12 (1979) 47 MR532376
18 R S Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982) 255 MR664497
19 R S Hamilton, Four-manifolds with positive curvature operator, J. Differential Geom. 24 (1986) 153 MR862046
20 R S Hamilton, The Ricci flow on surfaces, from: "Mathematics and general relativity (Santa Cruz, CA, 1986)" (editor J A Isenberg), Contemp. Math. 71, Amer. Math. Soc. (1988) 237 MR954419
21 T Ivey, Ricci solitons on compact three-manifolds, Differential Geom. Appl. 3 (1993) 301 MR1249376
22 B Kotschwar, On rotationally invariant shrinking Ricci solitons, Pacific J. Math. 236 (2008) 73 MR2398988
23 J Lauret, Ricci soliton homogeneous nilmanifolds, Math. Ann. 319 (2001) 715 MR1825405
24 A Lichnerowicz, Variétés kählériennes à première classe de Chern non negative et variétés riemanniennes à courbure de Ricci généralisée non negative, J. Differential Geometry 6 (1971) 47 MR0300228
25 J Lott, On the long-time behavior of type-III Ricci flow solutions, Math. Ann. 339 (2007) 627 MR2336062
26 R McOwen, Partial differential equations. Methods and applications, Prentice Hall (1996)
27 F Morgan, Manifolds with density, Notices Amer. Math. Soc. 52 (2005) 853 MR2161354
28 O Munteanu, N Sesum, On gradient Ricci solitons arXiv:0910.1105
29 A Naber, Noncompact shrinking 4–solitons with nonnegative curvature arXiv:0710.5579
30 L Ni, Ancient solutions to Kähler–Ricci flow, Math. Res. Lett. 12 (2005) 633 MR2189227
31 L Ni, N Wallach, On a classification of gradient shrinking solitons, Math. Res. Lett. 15 (2008) 941 MR2443993
32 G Perelman, The entropy formula for the Ricci flow and its geometric applications arXiv:math.DG/0211159
33 G Perelman, Ricci flow with surgery on three manifolds arXiv:math.DG/0303109
34 P Petersen, W Wylie, On gradient Ricci solitons with symmetry, Proc. Amer. Math. Soc. 137 (2009) 2085 MR2480290
35 P Petersen, W Wylie, Rigidity of gradient Ricci solitons, Pacific J. Math. 241 (2009) 329 MR2507581
36 G Wei, W Wylie, Comparison geometry for the Bakry–Emery Ricci tensor, J. Differential Geom. 83 (2009) 377 MR2577473
37 W Wylie, Complete shrinking Ricci solitons have finite fundamental group, Proc. Amer. Math. Soc. 136 (2008) 1803 MR2373611
38 S T Yau, Some function-theoretic properties of complete Riemannian manifold and their applications to geometry, Indiana Univ. Math. J. 25 (1976) 659 MR0417452
39 Z H Zhang, Gradient shrinking solitons with vanishing Weyl tensor, Pacific J. Math. 242 (2009) 189 MR2525510