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Ricci Flow with Surgery on ThreeManifolds
"... This is a technical paper, which is a continuation of [I]. Here we verify most of the assertions, made in [I, §13]; the exceptions are (1) the statement that a 3manifold which collapses with local lower bound for sectional curvature is a graph manifold this is deferred to a separate paper, as the ..."
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Cited by 448 (2 self)
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was considered by Hamilton [H 5,§4,5]; unfortunately, his argument, as written, contains an unjustified statement (RMAX = Γ, on page 62, lines 710 from the bottom), which I was unable to fix. Our approach is somewhat different, and is aimed at eventually constructing a canonical Ricci flow, defined on a largest
CANONICAL MEASURES AND KÄHLERRICCI FLOW
"... We show that the KählerRicci flow on an algebraic manifold of positive Kodaira dimension and semiample canonical line bundle converges to a unique canonical metric on its canonical model. It is also shown that there exists a canonical measure of analytic Zariski decomposition on an algebraic manif ..."
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Cited by 11 (1 self)
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We show that the KählerRicci flow on an algebraic manifold of positive Kodaira dimension and semiample canonical line bundle converges to a unique canonical metric on its canonical model. It is also shown that there exists a canonical measure of analytic Zariski decomposition on an algebraic
Strong uniqueness of the Ricci flow
 arXiv:0706.3081. HUAIDONG CAO
"... In this paper, we derive some local a priori estimates for Ricci flow. This gives rise to some strong uniqueness theorems. As a corollary, let g(t) be a smooth complete solution to the Ricci flow onR 3, with the canonical Euclidean metric E as initial data, then g(t) is trivial, i.e. g(t)≡E. 1 ..."
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Cited by 92 (0 self)
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In this paper, we derive some local a priori estimates for Ricci flow. This gives rise to some strong uniqueness theorems. As a corollary, let g(t) be a smooth complete solution to the Ricci flow onR 3, with the canonical Euclidean metric E as initial data, then g(t) is trivial, i.e. g(t)≡E. 1
The Canonical Expanding Soliton and Harnack inequalities for Ricci flow
, 2009
"... We introduce the notion of Canonical Expanding Ricci Soliton, and use it to derive new Harnack inequalities for Ricci flow. This viewpoint also gives geometric insight into the existing Harnack inequalities of Hamilton and Brendle. 1 ..."
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Cited by 11 (2 self)
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We introduce the notion of Canonical Expanding Ricci Soliton, and use it to derive new Harnack inequalities for Ricci flow. This viewpoint also gives geometric insight into the existing Harnack inequalities of Hamilton and Brendle. 1
The canonical shrinking soliton associated to a Ricci flow
 Calc. Var
"... Abstract To every Ricci flow on a manifold M over a time interval I ⊂ R−, we associate a shrinking Ricci soliton on the spacetime M×I. We relate properties of the original Ricci flow to properties of the new higherdimensional Ricci flow equipped with its own timeparameter. This geometric constru ..."
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Cited by 8 (2 self)
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Abstract To every Ricci flow on a manifold M over a time interval I ⊂ R−, we associate a shrinking Ricci soliton on the spacetime M×I. We relate properties of the original Ricci flow to properties of the new higherdimensional Ricci flow equipped with its own timeparameter. This geometric
Ricci flow on Kähler manifolds
, 2000
"... In the last two decades, the Ricci flow, introduced by R. Hamilton in [7], has been a subject of intense study. The Ricci flow provides an indispensable tool of deforming Riemannian metrics towards canonical metrics, such as Einstein ones. It is hoped that by deforming a metric to a canonical metric ..."
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Cited by 3 (1 self)
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In the last two decades, the Ricci flow, introduced by R. Hamilton in [7], has been a subject of intense study. The Ricci flow provides an indispensable tool of deforming Riemannian metrics towards canonical metrics, such as Einstein ones. It is hoped that by deforming a metric to a canonical
On the conditions to extend Ricci flow
 Dan Knopf) University of Texas
"... Consider {(M n, g(t)), 0 ≤ t < T < ∞} as an unnormalized Ricci flow solution: dgij = −2Rij for t ∈ [0, T). Richard Hamilton shows that if the dt curvature operator is uniformly bounded under the flow for all t ∈ [0, T) then the solution can be extended over T. Natasa Sesum proves that a unifor ..."
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Cited by 19 (5 self)
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which deforms Riemannian metrics in the direction of the Ricci tensor. One hopes that the Ricci flow will deform any Riemannian metric to some canonical metrics, such as Einstein metrics.
On the KählerRicci flow on projective manifolds of general type
 CHINESE ANN. MATH. SER. B
, 2006
"... This note concerns the global existence and convergence of the solution for KählerRicci flow equation when the canonical class, KX, is numerically effective and big. We clarify some known results regarding this flow on projective manifolds of general type and also show some new observations and r ..."
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Cited by 74 (21 self)
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This note concerns the global existence and convergence of the solution for KählerRicci flow equation when the canonical class, KX, is numerically effective and big. We clarify some known results regarding this flow on projective manifolds of general type and also show some new observations
Results 1  10
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