Corpus ID: 237941056

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

@inproceedings{Bru2021ConstancyOT,
  title={Constancy of the dimension in codimension one and locality of the unit normal on \$\mathrm\{RCD\}(K,N)\$ spaces},
  author={Elia Bru{\'e} and Enrico Pasqualetto and Daniele Semola},
  year={2021}
}
The aim of this paper is threefold. We first prove that, on RCD(K, N) spaces, the boundary measure of any set with finite perimeter is concentrated on the n-regular set Rn, where n ≤ N is the essential dimension of the space. After, we discuss localization properties of the unit normal providing representation formulae for the perimeter measure of intersections and unions of sets with finite perimeter. Finally, we study Gauss-Green formulae for essentially bounded divergence measure vector… Expand
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References

SHOWING 1-10 OF 49 REFERENCES
Rigidity of the 1-Bakry–Émery Inequality and Sets of Finite Perimeter in RCD Spaces
This note is dedicated to the study of the asymptotic behaviour of sets of finite perimeter over RCD(K,N) metric measure spaces. Our main result asserts existence of a Euclidean tangent half-spaceExpand
Rectifiability of the reduced boundary for sets of finite perimeter over $\RCD(K,N)$ spaces.
This note is devoted to the study of sets of finite perimeter over $\RCD(K,N)$ metric measure spaces. Its aim is to complete the picture about the generalization of De Giorgi's theorem within thisExpand
H\"older continuity of tangent cones in RCD(K,N) spaces and applications to non-branching
In this paper we prove that a metric measure space $(X,d,m)$ satisfying the finite Riemannian curvature-dimension condition ${\sf RCD}(K,N)$ is non-branching and that tangent cones from the sameExpand
Structure theory of metric measure spaces with lower Ricci curvature bounds
We prove that a metric measure space (X,d,m) satisfying finite dimensional lower Ricci curvature bounds and whose Sobolev space W1,2 is Hilbert is rectifiable. That is, a RCD∗(K,N)-space isExpand
Constancy of the Dimension for RCD( K , N ) Spaces via Regularity of Lagrangian Flows
We prove a regularity result for Lagrangian flows of Sobolev vector fields over RCD(K,N) metric measure spaces, regularity is understood with respect to a newly defined quasi-metric built from theExpand
Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows
Aim of this paper is to discuss convergence of pointed metric measure spaces in absence of any compactness condition. We propose various definitions, show that all of them are equivalent and that forExpand
On the volume measure of non-smooth spaces with Ricci curvature bounded below
We prove that, given an $RCD^{*}(K,N)$-space $(X,d,m)$, then it is possible to $m$-essentially cover $X$ by measurable subsets $(R_{i})_{i\in \mathbb{N}}$ with the following property: for each $i$Expand
New formulas for the Laplacian of distance functions and applications
The goal of the paper is to prove an exact representation formula for the Laplacian of the distance (and more generally for an arbitrary 1-Lipschitz function) in the framework of metric measureExpand
New stability results for sequences of metric measure spaces with uniform Ricci bounds from below
The aim of this paper is to provide new stability results for sequences of metric measure spaces $(X_i,d_i,m_i)$ convergent in the measured Gromov-Hausdorff sense. By adopting the so-called extrinsicExpand
On the differential structure of metric measure spaces and applications
The main goals of this paper are: i) To develop an abstract differential calculus on metric measure spaces by investigating the duality relations between differentials and gradients of SobolevExpand
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