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Ricci solitons  the . . .
, 2008
"... We discuss some classification results for Ricci solitons, that is, self similar solutions of the Ricci Flow. New simpler proofs of some known results will be presented. In detail, we will take the equation point of view, trying to avoid the tools provided by ..."
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We discuss some classification results for Ricci solitons, that is, self similar solutions of the Ricci Flow. New simpler proofs of some known results will be presented. In detail, we will take the equation point of view, trying to avoid the tools provided by
RECENT PROGRESS ON RICCI SOLITONS
, 2009
"... In recent years, there has seen much interest and increased research activities in Ricci solitons. Ricci solitons are natural generalizations of Einstein metrics. They are also special solutions to Hamilton’s Ricci flow and play important roles in the singularity study of the Ricci flow. In this pap ..."
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Cited by 30 (0 self)
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In recent years, there has seen much interest and increased research activities in Ricci solitons. Ricci solitons are natural generalizations of Einstein metrics. They are also special solutions to Hamilton’s Ricci flow and play important roles in the singularity study of the Ricci flow
REMARKS ON GRADIENT RICCI SOLITONS
, 2004
"... Abstract. In this paper, we study the gradient Ricci soliton equation on a complete Riemannian manifold. We show that under a natural decay condition on the Ricci curvature, the Ricci soliton is Ricciflat and ALE. 1. ..."
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Abstract. In this paper, we study the gradient Ricci soliton equation on a complete Riemannian manifold. We show that under a natural decay condition on the Ricci curvature, the Ricci soliton is Ricciflat and ALE. 1.
DEGENERATION OF SHRINKING RICCI SOLITONS
, 2009
"... Let (Y, d) be a GromovHausdorff limit of closed shrinking Ricci solitons with uniformly upper bounded diameter and lower bounded volume. We prove that off a closed subset of codimension at least 2, Y is a smooth manifold satisfying a shrinking Ricci soliton equation. ..."
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Cited by 6 (1 self)
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Let (Y, d) be a GromovHausdorff limit of closed shrinking Ricci solitons with uniformly upper bounded diameter and lower bounded volume. We prove that off a closed subset of codimension at least 2, Y is a smooth manifold satisfying a shrinking Ricci soliton equation.
RIGIDITY OF GRADIENT RICCI SOLITONS
, 2007
"... We define a gradient Ricci soliton to be rigid if it is a flat bundle N×ΓR k where N is Einstein. It is known that not all gradient solitons are rigid. Here we offer several natural conditions on the curvature that characterize rigid gradient solitons. Other related results on rigidity of Ricci soli ..."
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Cited by 34 (3 self)
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We define a gradient Ricci soliton to be rigid if it is a flat bundle N×ΓR k where N is Einstein. It is known that not all gradient solitons are rigid. Here we offer several natural conditions on the curvature that characterize rigid gradient solitons. Other related results on rigidity of Ricci
A note on Ricci solitons
"... Abstract. In this paper we consider a complete connected Ricci soliton (M, g, ξ, λ) of positive Ricci curvature and assign the Ricci tensor Ric = g, a role of another Riemannian metric on M. It is shown that the identity map i: (M, g) → (M, g) is a harmonic map. In addition, we also study compact s ..."
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Cited by 1 (1 self)
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Abstract. In this paper we consider a complete connected Ricci soliton (M, g, ξ, λ) of positive Ricci curvature and assign the Ricci tensor Ric = g, a role of another Riemannian metric on M. It is shown that the identity map i: (M, g) → (M, g) is a harmonic map. In addition, we also study compact
On gradient Ricci solitons with symmetry
"... We study gradient Ricci solitons with maximal symmetry. First we show that there are no nontrivial homogeneous gradient Ricci solitons. Thus the most symmetry one can expect is an isometric cohomogeneity one group action. Many examples of cohomogeneity one gradient solitons have been constructed. ..."
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Cited by 33 (5 self)
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We study gradient Ricci solitons with maximal symmetry. First we show that there are no nontrivial homogeneous gradient Ricci solitons. Thus the most symmetry one can expect is an isometric cohomogeneity one group action. Many examples of cohomogeneity one gradient solitons have been constructed
On Ricci solitons of cohomogeneity one
, 2008
"... We analyse some properties of the cohomogeneity one Ricci soliton equations, and use Ansätze of cohomogeneity one type to produce new explicit examples of complete Kähler Ricci solitons of expanding, steady and shrinking types. These solitons are foliated by hypersurfaces which are circle bundles ov ..."
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Cited by 26 (7 self)
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We analyse some properties of the cohomogeneity one Ricci soliton equations, and use Ansätze of cohomogeneity one type to produce new explicit examples of complete Kähler Ricci solitons of expanding, steady and shrinking types. These solitons are foliated by hypersurfaces which are circle bundles
Stability and instability of Ricci solitons
"... We consider the volumenormalized Ricci flow close to compact shrinking Ricci solitons. We show that if a compact Ricci soliton (M, g) is a local maximum of Perelman’s shrinker entropy, any normalized Ricci flow starting close to it exists for all time and converges towards a Ricci soliton. If g is ..."
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We consider the volumenormalized Ricci flow close to compact shrinking Ricci solitons. We show that if a compact Ricci soliton (M, g) is a local maximum of Perelman’s shrinker entropy, any normalized Ricci flow starting close to it exists for all time and converges towards a Ricci soliton. If g
GENERALISED RICCI SOLITONS
"... Abstract. We introduce a class of overdetermined systems of partial differential equations of finite type on (pseudo)Riemannian manifolds that we call the generalised Ricci soliton equations. These equations depend on three real parameters. For special values of the parameters they specialise to v ..."
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Abstract. We introduce a class of overdetermined systems of partial differential equations of finite type on (pseudo)Riemannian manifolds that we call the generalised Ricci soliton equations. These equations depend on three real parameters. For special values of the parameters they specialise
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