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

Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Length, area, volume, other geometric measure theory (28A75) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Functions of bounded variation, generalizations (26A45)

Cites Work

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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
On the differentiability of Lipschitz functions with respect to measures in the Euclidean space
On the structure of ${\mathcal A}$-free measures and applications
Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces
Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in $\text{RCD}(K, \infty)$ metric measure spaces
Pointwise properties of functions of bounded variation in metric spaces
Sharp Hölder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications
Functions of bounded variation on ``good metric spaces
Regularity of Einstein manifolds and the codimension 4 conjecture
On the relaxation in $BV(\Omega ;\mathbb{R}^ m)$ of quasi-convex integrals
Differentiability of Lipschitz functions on metric measure spaces
Rectifiable sets in metric and Banach spaces
Fine properties of sets of finite perimeter in doubling metric measure spaces
Lecture notes on differential calculus on $\mathsf{RCD}$ spaces
Rank-one theorem and subgraphs of BV functions in Carnot groups
Ricci tensor on $\mathrm{RCD}^\ast(K,N)$ spaces
Short-time behavior of the heat kernel and Weyl's law on $\mathrm{RCD}^*(K,N)$ spaces
Behaviour of the reference measure on $\mathsf{RCD}$ spaces under charts
Characterising rectifiable metric spaces using tangent spaces
Boundary regularity and stability for spaces with Ricci bounded below
Quasi-continuous vector fields on RCD spaces
Equivalent definitions of $BV$ space and of total variation on metric measure spaces
Rigidity of the 1-Bakry-Émery inequality and sets of finite Perimeter in RCD spaces
Tensorization of Cheeger energies, the space $H^{1, 1}$ and the area formula for graphs
Structure theory of metric measure spaces with lower Ricci curvature bounds
Cheeger-harmonic functions in metric measure spaces revisited
Rectifiability of the reduced boundary for sets of finite perimeter over $\operatorname{RCD} ( K , N )$ spaces
On the differential structure of metric measure spaces and applications
Characterizations of rectifiable metric measure spaces
Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows
Rank one property for derivatives of functions with bounded variation
Non-collapsed spaces with Ricci curvature bounded from below
On the volume measure of non-smooth spaces with Ricci curvature bounded below
Nonsmooth differential geometry– An approach tailored for spaces with Ricci curvature bounded from below
Rectifiability
Metric Rectifiability of ℍ-regular Surfaces with Hölder Continuous Horizontal Normal
On a conjecture of Cheeger
Constancy of the Dimension for RCD(K,N) Spaces via Regularity of Lagrangian Flows
Sobolev Spaces on Metric Measure Spaces
Structure of measures in Lipschitz differentiability spaces
Some fine properties of sets of finite perimeter in Ahlfors regular metric measure spaces
Rectifiability and perimeter in the Heisenberg group
Constancy of the dimension in codimension one and locality of the unit normal on $\RCD(K,N)$ spaces
Calculus and fine properties of functions of bounded variation on RCD spaces

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