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Volume Bounds for the Quantitative Singular Strata of Non Collapsed RCD Metric Measure Spaces

- Gioacchino Antonelli, Elia Brué, Daniele Semola
- Mathematics
- 1 January 2019

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 non… Expand

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 collapsed… Expand

Pauls rectifiable and purely Pauls unrectifiable smooth hypersurfaces

- Gioacchino Antonelli, Enrico Le Donne
- Mathematics
- 28 October 2019

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 in… Expand

On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth

- Gioacchino Antonelli, Elia Brué, Mattia Fogagnolo, Marco Pozzetta
- Mathematics
- 15 July 2021

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 sufficient… Expand

Distributional solutions of Burgers' type equations for intrinsic graphs in Carnot groups of step 2

- Gioacchino Antonelli, Daniela Di Donato, Sebastiano Don
- Mathematics
- 2 August 2020

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 function… Expand

On rectifiable measures in Carnot groups: structure theory

- Gioacchino Antonelli, Andrea Merlo
- Mathematics
- 29 September 2020

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 finite… Expand

On rectifiable measures in Carnot groups: representation

- Gioacchino Antonelli, Andrea Merlo
- Mathematics
- 1 April 2021

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 groups… Expand

Characterizations of uniformly differentiable co-horizontal intrinsic graphs in Carnot groups

- Gioacchino Antonelli, Daniela Di Donato, Sebastiano Don, Enrico Le Donne
- Mathematics
- 22 May 2020

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 main… Expand

The isoperimetric problem on Riemannian manifolds via Gromov-Hausdorff asymptotic analysis

- Gioacchino Antonelli, Mattia Fogagnolo, Marco Pozzetta
- Mathematics
- 29 January 2021

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 connected… Expand

Polynomial and horizontally polynomial functions on Lie groups

- Gioacchino Antonelli, Enrico Le Donne
- Mathematics
- 27 November 2020

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-invariant… Expand

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