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On the longtime behavior of typeIII Ricci flow solutions
, 2005
"... We show that threedimensional homogeneous Ricci flow solutions that admit finitevolume quotients have longtime limits given by expanding solitons. We show that the same is true for a large class of fourdimensional homogeneous solutions. We give an extension of Hamilton’s compactness theorem tha ..."
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Cited by 49 (4 self)
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We show that threedimensional homogeneous Ricci flow solutions that admit finitevolume quotients have longtime limits given by expanding solitons. We show that the same is true for a large class of fourdimensional homogeneous solutions. We give an extension of Hamilton’s compactness theorem that does not assume a lower injectivity radius bound, in terms of Riemannian groupoids. Using this, we show that the longtime behavior of typeIII Ricci flow solutions is governed by the dynamics of an R +action on a compact space.
Dimensional reduction and the longtime behavior of Ricci flow
 COMM. MATH. HELV
, 2007
"... If g(t) is a threedimensional Ricci flow solution, with sectional curvatures that are O(t−1) and diameter that is O(t 1 2), then the pullback Ricci flow solution on the universal cover approaches a homogeneous expanding soliton. ..."
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Cited by 18 (4 self)
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If g(t) is a threedimensional Ricci flow solution, with sectional curvatures that are O(t−1) and diameter that is O(t 1 2), then the pullback Ricci flow solution on the universal cover approaches a homogeneous expanding soliton.
Precompactness of solutions to the Ricci flow in the absence of injectivity radius estimates
, 2003
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GLOBAL BEHAVIOR OF THE RICCI FLOW ON HOMOGENEOUS MANIFOLDS WITH TWO ISOTROPY SUMMANDS.
"... Abstract. In this paper we study the global behavior of the Ricci flow equation for two classes of homogeneous manifolds with two isotropy summands. Using methods of the qualitative theory of differential equations, we present the global phase portrait of such systems and derive some geometrical co ..."
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Cited by 1 (0 self)
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Abstract. In this paper we study the global behavior of the Ricci flow equation for two classes of homogeneous manifolds with two isotropy summands. Using methods of the qualitative theory of differential equations, we present the global phase portrait of such systems and derive some geometrical consequences on the structure of such manifolds under the action of the Ricci flow. 1.
Precompactness of solutions to the Ricci flow
, 2003
"... in the absence of injectivity radius estimates ..."
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