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We show that a three-dimensional steady gradient Ricci soliton which is asymptotic to the Bryant soliton in a suitable sense must be isometric to the Bryant soliton.
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2006
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2006
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2008
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S. Brendle and R. Schoen, Classification of manifolds with weakly 1 / 4 1/4 -pinched curvatures,
2008
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R.L. Bryant, Ricci flow solitons in dimension three with S O ( 3 ) SO(3) -symmetries,
Cited in the paper.
H.D. Cao and Q. Chen, On locally conformally flat gradient steady Ricci solitons,
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G. Catino and C. Mantegazza, Evolution of the Weyl tensor under the Ricci flow under the Ricci flow,
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G. Perelman, The entropy formula for the Ricci flow and its geometric applications,
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G. Perelman, Ricci flow with surgery on three-manifolds,
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G. Perelman, Finite extinction time for solutions to the Ricci flow on certain three-manifolds,
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P. Petersen and W. Wylie, On the classification of gradient Ricci solitons,
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S. Brendle and R. Schoen, Manifolds with 1 / 4 1/4 -pinched curvature are space forms,
2009
Later among the works it cites.
H. Guo, Area growth rate of the level surface of the potential function on the 3 3 -dimensional steady Ricci soliton,
2009
Later among the works it cites.
S. Brendle, Ricci Flow and the Sphere Theorem,
2010
Closest in time.
S. Brendle and R. Schoen, Curvature, sphere theorems, and the Ricci flow,
2011
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