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    • Plusieurs versions

    Quantitative Differentiation: A General Formulation

    Cheeger, Jeff
    Communications on Pure and Applied Mathematics, December 2012, Vol.65(12), pp.1641-1670 [Revue évaluée par les pairs]

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    Metric and comparison geometry

    Cheeger, Jeff
    Somerville Mass. : International Press
    2007
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    Titre: Metric and comparison geometry / ed. by Jeffrey Cheeger ang Karsten Grove
    Auteur: Cheeger, Jeff
    Editeur: Somerville Mass. : International Press
    Date: 2007
    Collation: 347 p. : ill.
    Collection: Surveys in differential geometry ; vol. 11
    Documents dans cette collection: Surveys in differential geometry
    Sujet RERO: Géométrie différentielle - Espaces métriques - Topologie
    Sujet RERO - forme: [Études diverses]
    Classification: ams 00
    ams 53
    IMATH C-9
    Identifiant: 9781571461179 (ISBN); http://catalogue.bnf.fr/ark:/12148/cb45048885b (URN)
    No RERO: R005413884
    Permalien:
    http://data.rero.ch/01-R005413884/html?view=FR_V1

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    Degeneration of Riemannian metrics under Ricci curvature bounds

    Cheeger, Jeff
    Pisa : Accademia Nazionale dei Lincei/Scuola Normale Superiore di Pisa
    2001
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    Titre: Degeneration of Riemannian metrics under Ricci curvature bounds / Jeff Cheeger
    Auteur: Cheeger, Jeff
    Editeur: Pisa : Accademia Nazionale dei Lincei/Scuola Normale Superiore di Pisa
    Date: 2001
    Collation: 77 p. ; 24 cm
    Collection: Lezioni Fermiane
    Documents dans cette collection: Lezioni Fermiane
    Classification: IMATH C-9
    Identifiant: 8876423044 (ISBN)
    No RERO: R003654080
    Permalien:
    http://data.rero.ch/01-R003654080/html?view=FR_V1

    • Plusieurs versions

    Structure Theory and Convergence in Riemannian Geometry

    Cheeger, Jeff
    Milan Journal of Mathematics, 2010, Vol.78(1), pp.221-264 [Revue évaluée par les pairs]

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    Lower bounds on Ricci curvature and quantitative behavior of singular sets

    Cheeger, Jeff, Naber, Aaron
    Inventiones mathematicae, 2013, Vol.191(2), pp.321-339 [Revue évaluée par les pairs]
    Springer Science & Business Media B.V.
    Disponible
    Plus…
    Titre: Lower bounds on Ricci curvature and quantitative behavior of singular sets
    Auteur: Cheeger, Jeff; Naber, Aaron
    Description: Let Y n denote the Gromov-Hausdorff limit $M^{n}_{i}\stackrel{d_{\mathrm{GH}}}{\longrightarrow} Y^{n}$ of v-noncollapsed Riemannian manifolds with ${\mathrm{Ric}}_{M^{n}_{i}}\geq-(n-1)$ . The singular set $\mathcal {S}\subset Y$ has a stratification $\mathcal {S}^{0}\subset \mathcal {S}^{1}\subset\cdots\subset \mathcal {S}$ , where $y\in \mathcal {S}^{k}$ if no tangent cone at y splits off a factor ℝ k +1 isometrically. Here, we define for all η >0, 0< r ≤1, the k-th effective singular stratum $\mathcal {S}^{k}_{\eta,r}$ satisfying $\bigcup_{\eta}\bigcap_{r} \,\mathcal {S}^{k}_{\eta,r}= \mathcal {S}^{k}$ . Sharpening the known Hausdorff dimension bound $\dim\, \mathcal {S}^{k}\leq k$ , we prove that for all y , the volume of the r -tubular neighborhood of $\mathcal {S}^{k}_{\eta,r}$ satisfies ${\mathrm {Vol}}(T_{r}(\mathcal {S}^{k}_{\eta,r})\cap B_{\frac{1}{2}}(y))\leq c(n,{\mathrm {v}},\eta)r^{n-k-\eta}$ . The proof involves a quantitative differentiation argument. This result has applications to Einstein manifolds. Let $\mathcal {B}_{r}$ denote the set of points at which the C 2 -harmonic radius is ≤ r . If also the $M^{n}_{i}$ are Kähler-Einstein with L 2 curvature bound, $\| Rm\|_{L_{2}}\leq C$ , then ${\mathrm {Vol}}( \mathcal {B}_{r}\cap B_{\frac{1}{2}}(y))\leq c(n,{\mathrm {v}},C)r^{4}$ for all y . In the Kähler-Einstein case, without assuming any integral curvature bound on the $M^{n}_{i}$ , we obtain a slightly weaker volume bound on $\mathcal {B}_{r}$ which yields an a priori L p curvature bound for all p
    Fait partie de: Inventiones mathematicae, 2013, Vol.191(2), pp.321-339
    Identifiant: 0020-9910 (ISSN); 1432-1297 (E-ISSN); 10.1007/s00222-012-0394-3 (DOI)

    • Plusieurs versions

    Realization of Metric Spaces as Inverse Limits, and Bilipschitz Embedding in L 1

    Cheeger, Jeff, Kleiner, Bruce
    Geometric and Functional Analysis, 2013, Vol.23(1), pp.96-133 [Revue évaluée par les pairs]

    • Plusieurs versions

    Inverse Limit Spaces Satisfying a Poincaré Inequality

    Cheeger Jeff, Kleiner Bruce
    Analysis and Geometry in Metric Spaces, 01 January 2015, Vol.3(1) [Revue évaluée par les pairs]

    • Plusieurs versions

    Quantitative Stratification and the Regularity of Harmonic Maps and Minimal Currents

    Cheeger, Jeff, Naber, Aaron
    Communications on Pure and Applied Mathematics, June 2013, Vol.66(6), pp.965-990 [Revue évaluée par les pairs]

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    Lower bounds on Ricci curvature and quantitative behavior of singular sets

    Cheeger, Jeff, Naber, Aaron
    Inventiones mathematicae, 2/2013, Vol.191(2), pp.321-339 [Revue évaluée par les pairs]
    Springer (via CrossRef)
    Disponible
    Plus…
    Titre: Lower bounds on Ricci curvature and quantitative behavior of singular sets
    Auteur: Cheeger, Jeff; Naber, Aaron
    Sujet: Anatomy & Physiology ; Mathematics;
    Description: Let Y n denote the Gromov-Hausdorff limit \(M^{n}_{i}\stackrel{d_{\mathrm{GH}}}{\longrightarrow} Y^{n}\) of v-noncollapsed Riemannian manifolds with \({\mathrm{Ric}}_{M^{n}_{i}}\geq-(n-1)\). The singular set \(\mathcal {S}\subset Y\) has a stratification \(\mathcal {S}^{0}\subset \mathcal {S}^{1}\subset\cdots\subset \mathcal {S}\), where \(y\in \mathcal {S}^{k}\) if no tangent cone at y splits off a factor ℝk+1 isometrically. Here, we define for all η>0, 0
    Fait partie de: Inventiones mathematicae, 2/2013, Vol.191(2), pp.321-339
    Identifiant: 0020-9910 (ISSN); 1432-1297 (E-ISSN); http (DOI)

    • Plusieurs versions

    Comparison theorems in Riemannian geometry

    Cheeger, Jeff