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Volume Bounds for the Quantitative Singular Strata of Non Collapsed RCD Metric Measure Spaces
Abstract The aim of this note is to generalize to the class of non collapsed RCD(K, N) metric measure spaces the volume bound for the effective singular strata obtained by Cheeger and Naber for nonExpand
J ul 2 01 9 Volume bounds for the quantitative singular strata of non collapsed RCD metric measure spaces
The aim of this note is to generalize to the class of non collapsed RCD(K, N) metric measure spaces the volume bound for the effective singular strata obtained by Cheeger and Naber for non collapsedExpand
Pauls rectifiable and purely Pauls unrectifiable smooth hypersurfaces
This paper is related to the problem of finding a good notion of rectifiability in sub-Riemannian geometry. In particular, we study which kind of results can be expected for smooth hypersurfaces inExpand
On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth
In this paper we provide new existence results for isoperimetric sets of large volume in Riemannian manifolds with nonnegative Ricci curvature and Euclidean volume growth. We find sufficientExpand
Distributional solutions of Burgers' type equations for intrinsic graphs in Carnot groups of step 2
We prove that in arbitrary Carnot groups $\mathbb G$ of step 2, with a splitting $\mathbb G=\mathbb W\cdot\mathbb L$ with $\mathbb L$ one-dimensional, the graph of a continuous functionExpand
On rectifiable measures in Carnot groups: structure theory
In this paper we prove the one-dimensional Preiss' theorem in the first Heisenberg group $\mathbb H^1$. More precisely we show that a Radon measure $\phi$ on $\mathbb H^1$ with positive and finiteExpand
On rectifiable measures in Carnot groups: representation
This paper deals with the theory of rectifiability in arbitrary Carnot groups, and in particular with the study of the notion of P-rectifiable measure. First, we show that in arbitrary Carnot groupsExpand
Characterizations of uniformly differentiable co-horizontal intrinsic graphs in Carnot groups
In arbitrary Carnot groups we study intrinsic graphs of maps with horizontal target. These graphs are $C^1_H$ regular exactly when the map is uniformly intrinsically differentiable. Our first mainExpand
The isoperimetric problem on Riemannian manifolds via Gromov-Hausdorff asymptotic analysis
In this paper we prove the existence of isoperimetric regions of any volume in Riemannian manifolds with Ricci bounded below assuming Gromov–Hausdorff asymptoticity to the suitable simply connectedExpand
Polynomial and horizontally polynomial functions on Lie groups
We generalize both the notion of polynomial functions on Lie groups and the notion of horizontally affine maps on Carnot groups. We fix a subset $S$ of the algebra $\mathfrak g$ of left-invariantExpand
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