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Classification of expanding and steady Ricci solitons with integral curvature decay

Giovanni Catino, Paolo Mastrolia and Dario D Monticelli

Geometry & Topology 20 (2016) 2665–2685
Bibliography
1 S Bando, Real analyticity of solutions of Hamilton’s equation, Math. Z. 195 (1987) 93 MR888130
2 J Bernstein, T Mettler, Two-dimensional gradient Ricci solitons revisited, Int. Math. Res. Not. 2015 (2015) 78 MR3340295
3 J P Bourguignon, H Karcher, Curvature operators: pinching estimates and geometric examples, Ann. Sci. École Norm. Sup. 11 (1978) 71 MR0493867
4 S Brendle, Rotational symmetry of self-similar solutions to the Ricci flow, Invent. Math. 194 (2013) 731 MR3127066
5 R L Bryant, Ricci flow solitons in dimension three with SO(3)–symmetries, preprint (2005)
6 H D Cao, G Catino, Q Chen, C Mantegazza, L Mazzieri, Bach-flat gradient steady Ricci solitons, Calc. Var. Partial Differential Equations 49 (2014) 125 MR3148109
7 H D Cao, B L Chen, X P Zhu, Recent developments on Hamilton’s Ricci flow, from: "Surveys in differential geometry, XII : Geometric flows" (editors H D Cao, S T Yau), Surv. Differ. Geom. 12, International Press (2008) 47 MR2488948
8 H D Cao, C He, Infinitesimal rigidity of collapsed gradient steady Ricci solitons in dimension three, preprint (2014) arXiv:1412.2714v1
9 G Catino, Complete gradient shrinking Ricci solitons with pinched curvature, Math. Ann. 355 (2013) 629 MR3010141
10 G Catino, Some rigidity results on critical metrics for quadratic functionals, Calc. Var. Partial Differential Equations 54 (2015) 2921 MR3412398
11 G Catino, C Mantegazza, L Mazzieri, A note on Codazzi tensors, Math. Ann. 362 (2015) 629 MR3343892
12 G Catino, P Mastrolia, D D Monticelli, M Rigoli, Analytic and geometric properties of generic Ricci solitons, Trans. Amer. Math. Soc. 368 (2016) 7533 MR3546774
13 G Catino, L Mazzieri, S Mongodi, Rigidity of gradient Einstein shrinkers, Commun. Contemp. Math. 17 (2015) 1550046, 18 MR3485875
14 B L Chen, Strong uniqueness of the Ricci flow, J. Differential Geom. 82 (2009) 363 MR2520796
15 C W Chen, A Deruelle, Structure at infinity of expanding gradient Ricci soliton, Asian J. Math. 19 (2015) 933 MR3431684
16 O Chodosh, Expanding Ricci solitons asymptotic to cones, Calc. Var. Partial Differential Equations 51 (2014) 1 MR3247379
17 B Chow, P Lu, L Ni, Hamilton’s Ricci flow, 77, Amer. Math. Soc. (2006) MR2274812
18 A Deruelle, Steady gradient Ricci soliton with curvature in L1, Comm. Anal. Geom. 20 (2012) 31 MR2903100
19 A Deruelle, Asymptotic estimates and compactness of expanding gradient Ricci solitons, preprint (2014) arXiv:1411.2366v1
20 M Eminenti, G La Nave, C Mantegazza, Ricci solitons: the equation point of view, Manuscripta Math. 127 (2008) 345 MR2448435
21 R S Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982) 255 MR664497
22 R S Hamilton, The Ricci flow on surfaces, from: "Mathematics and general relativity" (editor J A Isenberg), Contemp. Math. 71, Amer. Math. Soc. (1988) 237 MR954419
23 R S Hamilton, The formation of singularities in the Ricci flow, from: "Surveys in differential geometry" (editor S T Yau), Int. Press (1995) 7 MR1375255
24 T Ivey, Ricci solitons on compact three-manifolds, Differential Geom. Appl. 3 (1993) 301 MR1249376
25 S Kobayashi, K Nomizu, Foundations of differential geometry, I, John Wiley & Sons (1963) MR0152974
26 L Ma, Expanding Ricci solitons with pinched Ricci curvature, Kodai Math. J. 34 (2011) 140 MR2786787
27 P Mastrolia, M Rigoli, M Rimoldi, Some geometric analysis on generic Ricci solitons, Commun. Contemp. Math. 15 (2013) 1250058, 25 MR3063556
28 O Munteanu, J Wang, Geometry of shrinking Ricci solitons, Compos. Math. 151 (2015) 2273 MR3433887
29 L Ni, N Wallach, On a classification of gradient shrinking solitons, Math. Res. Lett. 15 (2008) 941 MR2443993
30 G Perelman, The entropy formula for the Ricci flow and its geometric applications, preprint (2002) arXiv:math/0211159v1
31 P Petersen, W Wylie, Rigidity of gradient Ricci solitons, Pacific J. Math. 241 (2009) 329 MR2507581
32 P Petersen, W Wylie, On the classification of gradient Ricci solitons, Geom. Topol. 14 (2010) 2277 MR2740647
33 S Pigola, M Rimoldi, A G Setti, Remarks on non-compact gradient Ricci solitons, Math. Z. 268 (2011) 777 MR2818729
34 F Schulze, M Simon, Expanding solitons with non-negative curvature operator coming out of cones, Math. Z. 275 (2013) 625 MR3101823
35 J Y Wu, P Wu, Heat kernel on smooth metric measure spaces with nonnegative curvature, Math. Ann. 362 (2015) 717 MR3368080
36 J Y Wu, P Wu, W Wylie, Gradient shrinking Ricci solitons of half harmonic Weyl curvature, preprint (2014) arXiv:1410.7303v1