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46
Collapsing riemannian manifolds while keeping their curvature bounded
 I, J. Differential Geometry
, 1986
"... This is the second of two papers concerned with the situation in which the injectivity radius at certain points of a riemannian manifold is "small" compared to the curvature. In Part I [3], we introduced the concept of an Fstructure of positive ..."
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Cited by 91 (5 self)
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This is the second of two papers concerned with the situation in which the injectivity radius at certain points of a riemannian manifold is "small" compared to the curvature. In Part I [3], we introduced the concept of an Fstructure of positive
On the structure of spaces with Ricci curvature bounded below. I
 J. DIFFERENTIAL GEOM
, 1997
"... ..."
Curvature And Symmetry Of Milnor Spheres
 Ann. of Math
"... this paper to also analyze bundles with base CP CP # CP , and S ..."
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Cited by 78 (17 self)
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this paper to also analyze bundles with base CP CP # CP , and S
Almost flat manifolds
 J. Differential Geometry
, 1978
"... 1.1. We denote by V a connected ^dimensional complete Riemannian manifold, by d = d(V) the diameter of V, and by c + = c + (V) and c ~ = c~(V), respectively, the upper and lower bounds of the sectional curvature of V. We set c = c(V) = max (  c + 1,  c ~ ). ..."
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Cited by 49 (1 self)
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1.1. We denote by V a connected ^dimensional complete Riemannian manifold, by d = d(V) the diameter of V, and by c + = c + (V) and c ~ = c~(V), respectively, the upper and lower bounds of the sectional curvature of V. We set c = c(V) = max (  c + 1,  c ~ ).
Scalar curvature and geometrization conjectures for 3manifolds
 in Comparison Geometry (Berkeley 1993–94), MSRI Publications
, 1997
"... Abstract. We first summarize very briefly the topology of 3manifolds and the approach of Thurston towards their geometrization. After discussing some general properties of curvature functionals on the space of metrics, we formulate and discuss three conjectures that imply Thurston’s Geometrization ..."
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Cited by 31 (9 self)
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Abstract. We first summarize very briefly the topology of 3manifolds and the approach of Thurston towards their geometrization. After discussing some general properties of curvature functionals on the space of metrics, we formulate and discuss three conjectures that imply Thurston’s Geometrization Conjecture for closed oriented 3manifolds. The final two sections present evidence for the validity of these conjectures and outline an approach toward their proof.
Diffeomorphism finiteness, positive pinching, and second homotopy
 Geom. Funct. Anal
, 1999
"... ..."
Convergence theorems in Riemannian geometry
 COMPARISON GEOMETRY
, 1997
"... This is a survey on the convergence theory developed rst by Cheeger and Gromov. In their theory one is concerned with the compactness of the class of riemannian manifolds with bounded curvature and lower bound on the injectivity radius. We explain and give proofs of almost all the major results, inc ..."
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Cited by 20 (0 self)
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This is a survey on the convergence theory developed rst by Cheeger and Gromov. In their theory one is concerned with the compactness of the class of riemannian manifolds with bounded curvature and lower bound on the injectivity radius. We explain and give proofs of almost all the major results, including Anderson's generalizations to the case where all one has is bounded Ricci curvature. The exposition is streamlined by the introduction of a norm for riemannian manifolds, which makes the theory more like that of Holder and Sobolev spaces.
On Stationary Vacuum Solutions To The Einstein Equations
, 1999
"... this paper is that in fact there are no such nontrivial stationary spacetimes; this of course places the physical reasoning above on stronger footing ..."
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Cited by 15 (8 self)
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this paper is that in fact there are no such nontrivial stationary spacetimes; this of course places the physical reasoning above on stronger footing
HamiltonPerelman’s Proof of the Poincaré Conjecture and The Geometrization Conjecture
, 2006
"... In this paper, we provide an essentially selfcontained and detailed account of the fundamental works of Hamilton and the recent breakthrough of Perelman on the Ricci flow and their application to the geometrization of threemanifolds. In particular, we give a detailed exposition of a complete pro ..."
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Cited by 15 (0 self)
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In this paper, we provide an essentially selfcontained and detailed account of the fundamental works of Hamilton and the recent breakthrough of Perelman on the Ricci flow and their application to the geometrization of threemanifolds. In particular, we give a detailed exposition of a complete proof of the Poincaré conjecture due to Hamilton and Perelman.