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Curvature, Sphere Theorems, and the Ricci flow (Q3067003)

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Language	Label	Description	Also known as
English	Curvature, Sphere Theorems, and the Ricci flow	scientific article

Statements

scholarly article

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Curvature, Sphere Theorems, and the Ricci flow (English)

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zbMATH Open document ID

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10.1090/S0273-0979-2010-01312-4

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Richard M. Schoen

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Bulletin of the American Mathematical Society

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publication date

20 January 2011

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full work available at URL

https://arxiv.org/abs/1001.2278

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Mathematics Subject Classification ID

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zbMATH DE Number

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zbMATH Keywords

pinched curvature

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sphere theorem

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Hamilton's Ricci flow

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MaRDI profile type

MaRDI publication profile

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A sphere theorem with a pinching constant below \({1\over 4}\)

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An infinite family of distinct 7-manifolds admitting positively curved Riemannian structures

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Contraction of convex hypersurfaces in Riemannian spaces

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Four-manifolds with \(1/4\)-pinched flag curvatures

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On the classification of three-dimensional compact Kähler manifolds of nonnegative bisectional curvature

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On a certain family of closed 13-dimensional Riemannian manifolds of positive curvature

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From vanishing theorems to estimating theorems: the Bochner technique revisited

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Les variétés riemanniennes homogenes simplement connexes de dimension impaire à courbure strictement positive

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Sur les groupes d'holonomie homogènes de variétés à connexion affine et des variétés riemanniennes

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Sur quelques variétés riemanniennes suffisamment pincées

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Sur quelques variétés d'Einstein compactes

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Sur les variétés riemanniennes pincées juste au-dessous de 1/4

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A Panoramic View of Riemannian Geometry

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Einstein manifolds

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Manifolds with positive curvature operators are space forms

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Principe du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérées

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A general convergence result for the Ricci flow in higher dimensions

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A generalization of Hamilton's differential Harnack inequality for the Ricci flow

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Einstein manifolds with nonnegative isotropic curvature are locally symmetric

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Einstein metrics and preserved curvature conditions for the Ricci flow

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Ancient solutions to the Ricci flow with pinched curvature

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Manifolds with 1/4-pinched curvature are space forms

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Classification of manifolds with weakly 1/4-pinched curvatures

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Sphere Theorems in Geometry

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EXAMPLES OF SINGULAR NORMAL COMPLEX SPACES WHICH ARE TOPOLOGICAL MANIFOLDS

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Beispiele zur Differentialtopologie von Singularitäten

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On Harnack's inequalities for the Kähler-Ricci flow

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Certain 4-manifolds with non-negative sectional curvature

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AN INTRINSIC PROOF OF GROMOLL–GROVE DIAMETER RIGIDITY THEOREM

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Some new four-manifolds

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A conformally invariant sphere theorem in four dimensions

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On the structure of spaces with Ricci curvature bounded below. I

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Complete Riemannian manifolds with pointwise pinched curvature

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Pointwise 1/4-pinched 4-manifolds

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Deforming metrics in the direction of their Ricci tensors

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New examples of manifolds with strictly positive curvature

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Local convexity and nonnegative curvature - Gromov's proof of the sphere theorem

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Almost positive curvature on the Gromoll-Meyer sphere

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Negatively Curved Manifolds with Exotic Smooth Structures

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The sigma model (dual) representation for a two-parameter family of integrable quantum field theories

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An exotic free involution on \(S^ 4\).

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Fundamental groups of manifolds with positive isotropic curvature

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The topology of four-dimensional manifolds

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On the topology of manifolds with positive isotropic curvature

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Differenzierbare Strukturen und Metriken positiver Krümmung auf Sphären

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A generalization of Berger's rigidity theorem for positively curved manifolds

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An exotic sphere with nonnegative sectional curvature

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Curvature, diameter and Betti numbers

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Sign and geometric meaning of curvature

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Local and superlinear convergence of a primal-dual interior point method for nonlinear semidefinite programming

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Pinching constants for hyperbolic manifolds

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Group actions and curvature

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Jacobi fields and Finsler metrics on compact Lie groups with an application to differentiable pinching problems

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A generalized sphere theorem

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A new proof of Mok’s generalized Frankel conjecture theorem

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On Einstein manifolds of positive sectional curvature

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Three-manifolds with positive Ricci curvature

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Four-manifolds with positive curvature operator

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The Harnack estimate for the Ricci flow

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Eternal solutions to the Ricci flow

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Convex hypersurfaces with pinched second fundamental form

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Four-manifolds with positive isotropic curvature

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Harmonic spinors

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On the topology of positively curved 4-manifolds with symmetry

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Ricci deformation of the metric on a Riemannian manifold

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An equivariant pinching theorem

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Exotic spheres and curvature

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Groups of homotopy spheres. I

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Über Riemannsche Mannigfaltigkeiten mit positiver Krümmung

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A sharp characterization of the smooth 4-sphere in curvature terms

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Non-negative Ricci curvature on closed manifolds under Ricci flow

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Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two-planes

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Metrics with nonnegative isotropic curvature

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On manifolds homeomorphic to the 7-sphere

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The uniformization theorem for compact Kähler manifolds of nonnegative holomorphic bisectional curvature

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Isotropic Curvature and the Ricci Flow

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Complete manifolds with nonnegative curvature operator

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A new version of differentiable sphere theorem

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Manifolds of Positive Ricci Curvature with Almost Maximal Volume

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Classification of almost quarter-pinched manifolds

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A contribution to differential geometry in the large

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Krümmung und differenzierbare Struktur auf Sphären. II

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Riemannian manifolds with bounded curvature ratios

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A pinching theorem for four manifolds

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Manifolds with nonnegative isotropic curvature

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Curvature tensor under the Ricci flow

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Compact Kähler manifolds of positive bisectional curvature

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Generalized Poincaré's conjecture in dimensions greater than four

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Simply connected manifolds of positive scalar curvature

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On the differentiable pinching problem. Improved by H. Karcher

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A theorem on Riemannian manifolds of positive curvature operator

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Les variétés riemanniennes de dimension 4 4/19-pincées. (4/19- pinched Riemannian manifolds of dimension 4)

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Compact homogeneous Riemannian manifolds with strictly positive curvature

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An exotic sphere with positive curvature almost everywhere.

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Rigidity of Einstein 4-manifolds with positive curvature

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Mathematics(1 entry)

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