The rank-one theorem on $\mathrm{RCD}$ spaces (Q6631522)

scientific article; zbMATH DE number 7937647

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English	The rank-one theorem on $\mathrm{RCD}$ spaces	scientific article; zbMATH DE number 7937647

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scholarly article

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title

The rank-one theorem on $\mathrm{RCD}$ spaces (English)

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1 November 2024

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zbMATH Keywords

function of bounded variation

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rank-one theorem

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$\mathrm{RCD}$ space

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MaRDI profile type

Publication

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cites work

Rank one property for derivatives of functions with bounded variation

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Some fine properties of sets of finite perimeter in Ahlfors regular metric measure spaces

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Equivalent definitions of $BV$ space and of total variation on metric measure spaces

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Rectifiable sets in metric and Banach spaces

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Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces

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Tensorization of Cheeger energies, the space $H^{1, 1}$ and the area formula for graphs

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On the Bakry-Émery condition, the gradient estimates and the local-to-global property of $\mathrm{RCD}^*(K,N)$ metric measure spaces

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Short-time behavior of the heat kernel and Weyl's law on $\mathrm{RCD}^*(K,N)$ spaces

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Rigidity of the 1-Bakry-Émery inequality and sets of finite Perimeter in RCD spaces

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Structure of measures in Lipschitz differentiability spaces

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Characterising rectifiable metric spaces using tangent spaces

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Characterizations of rectifiable metric measure spaces

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Calculus and fine properties of functions of bounded variation on RCD spaces

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Constancy of the Dimension for RCD(<i>K</i>,<i>N</i>) Spaces via Regularity of Lagrangian Flows

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Boundary regularity and stability for spaces with Ricci bounded below

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Constancy of the dimension in codimension one and locality of the unit normal on $\RCD(K,N)$ spaces

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Rectifiability of the reduced boundary for sets of finite perimeter over $\operatorname{RCD} ( K , N )$ spaces

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Differentiability of Lipschitz functions on metric measure spaces

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Regularity of Einstein manifolds and the codimension 4 conjecture

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Sharp Hölder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications

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Non-collapsed spaces with Ricci curvature bounded from below

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Nonsmooth differential geometry– An approach tailored for spaces with Ricci curvature bounded from below

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Behaviour of the reference measure on $\mathsf{RCD}$ spaces under charts

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Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows

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Ricci tensor on $\mathrm{RCD}^\ast(K,N)$ spaces

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Cheeger-harmonic functions in metric measure spaces revisited

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On the volume measure of non-smooth spaces with Ricci curvature bounded below

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Pointwise properties of functions of bounded variation in metric spaces

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Rectifiability

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Functions of bounded variation on ``good'' metric spaces

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Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in $\text{RCD}(K, \infty)$ metric measure spaces

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Identifiers

Mathematics Subject Classification ID

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10.2140/APDE.2024.17.2797

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Sitelinks

Mathematics(1 entry)

mardi Publication:6631522

The rank-one theorem on \(\mathrm{RCD}\) spaces (Q6631522)

Statements

Identifiers

Sitelinks

Mathematics(1 entry)