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We show that the only complete shrinking gradient Ricci solitons with vanishing Weyl tensor are quotients of the standard ones.
An extension of E. Hopf’s maximum principle with an application to Riemannian geometry
E. Calabi · 1958
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Variétés kählériennes à première classe de Chern non negative et variétés riemanniennes à courbure de Ricci généralisée non negative
André Lichnerowicz · 1971
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Some function-theoretic properties of complete Riemannian manifold and their applications to geometry
S.T. Yau · 1976
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C ∞ C^{\infty} approximations of convex subharmonic and plurisubharmonic functions
R.E. Greene and H. Wu · 1979
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Three-manifolds with positive Ricci curvature
Richard Hamilton · 1982
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Four-manifolds with positive curvature operator
Richard Hamilton · 1986
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Einstein Manifolds
Arthur Besse · 1987
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The Ricci flow on surfaces
Richard Hamilton · 1988
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Pointwise 1 4 \frac{1}{4} -pinched 4 4 -manifolds
Haiwen Chen · 1991
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Ricci solitons on compact three-manifolds
Thomas Ivey · 1993
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The Formation of Singularities in the Ricci Flow
Richard Hamilton · 1995
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Lower bounds on Ricci curvature and the almost rigidity of warped products
Jeff Cheeger and Tobias Colding · 1996
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Partial Differential Equations. Prentice Hall, 1996
Robert McOwen · 1996
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Ricci soliton homogeneous nilmanifolds
Jorge Lauret · 2001
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The Ricci flow: an introduction
Ancient Solutions to Kähler Ricci flow
Lei Ni · 2005
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A note on uniformization of Riemann surfaces by Ricci flow
Xiuxiong Chen, Peng Lu, and Gang Tian · 2006
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Hamilton’s Ricci flow
Bennett Chow, Peng Lu, and Lei Ni · 2006
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Three-dimensional Ricci solitons which project to surfaces
Paul Baird and Laurent Danielo · 2007
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Nonnegatively curved manifolds with finite fundamental groups admit metrics with positive Ricci curvature
Christoph Böhm and Burkhard Wilking · 2007
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Compact Gradient Shrinking Ricci Solitons with Positive Curvature Operator
Xiadong Cao · 2007
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Bennet Chow and Dan Knopf · 2004
Cited alongside, same era.
Manifolds with Density
Frank Morgan · 2005
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Manifolds with positive curvature operators are space forms
Christoph Böhm and Burkhard Wilking
Cited in the paper.
Ricci Solitons - the Equation Point of View
Manolo Eminenti, Gabriele La Nave, and Carlo Mantegazza
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Noncompact shrinking 4 4 -solitons with nonnegative curvature
Aaron Naber
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On a classification of the gradient shrinking solitons
Lei Ni and Nolan Wallach
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On the long-time behavior of type-III Ricci flow solutions
John Lott · 2007
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Complete shrinking Ricci solitons have finite fundamental group
William Wylie · 2008
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