Uniformly rectifiable metric spaces: Lipschitz images, bi-lateral weak geometric lemma and corona decompositions
In their 1991 and 1993 foundational monographs, David and Semmes characterized uniform
rectifiability for subsets of Euclidean space in a multitude of geometric and analytic ways …
rectifiability for subsets of Euclidean space in a multitude of geometric and analytic ways …
Density of continuous functions in Sobolev spaces with applications to capacity
S Eriksson-Bique, P Poggi-Corradini - Transactions of the American …, 2024 - ams.org
We show that capacity can be computed with locally Lipschitz functions in locally complete
and separable metric spaces. Further, we show that if $(X, d,\mu) $ is a locally complete and …
and separable metric spaces. Further, we show that if $(X, d,\mu) $ is a locally complete and …
Intrinsically H\" older sections in metric spaces
D Di Donato - arXiv preprint arXiv:2205.02688, 2022 - arxiv.org
We introduce a notion of intrinsically H\" older graphs in metric spaces. Following a recent
paper of Le Donne and the author, we prove some relevant results as the Ascoli-Arzel\a …
paper of Le Donne and the author, we prove some relevant results as the Ascoli-Arzel\a …
On various Carleson-type geometric lemmas and uniform rectifiability in metric spaces
We introduce new flatness coefficients, which we call\emph {$\iota $-numbers}, for Ahlfors
regular sets in metric spaces. We investigate the relation between Carleson-type geometric …
regular sets in metric spaces. We investigate the relation between Carleson-type geometric …
[PDF][PDF] The Rank-One Theorem on spaces
G Antonelli, C Brena, E Pasqualetto - arXiv preprint arXiv:2204.04921, 2022 - arxiv.org
arXiv:2204.04921v1 [math.MG] 11 Apr 2022 Page 1 arXiv:2204.04921v1 [math.MG] 11 Apr
2022 THE RANK-ONE THEOREM ON RCD SPACES GIOACCHINO ANTONELLI, CAMILLO …
2022 THE RANK-ONE THEOREM ON RCD SPACES GIOACCHINO ANTONELLI, CAMILLO …
On 1-regular and 1-uniform metric measure spaces
D Bate - arXiv preprint arXiv:2501.05920, 2025 - arxiv.org
A metric measure space $(X,\mu) $ is 1-regular if\[0<\lim_ {r\to 0}\frac {\mu (B (x, r))}{r}<\infty\]
for $\mu $-ae $ x\in X $. We give a complete geometric characterisation of the rectifiable and …
for $\mu $-ae $ x\in X $. We give a complete geometric characterisation of the rectifiable and …
Failure of the curvature-dimension condition in sub-Finsler manifolds
M Magnabosco, T Rossi - arXiv preprint arXiv:2307.01820, 2023 - arxiv.org
The Lott-Sturm-Villani curvature-dimension condition $\mathsf {CD}(K, N) $ provides a
synthetic notion for a metric measure space to have curvature bounded from below by $ K …
synthetic notion for a metric measure space to have curvature bounded from below by $ K …
Identifying 1-rectifiable measures in Carnot groups
We continue to develop a program in geometric measure theory that seeks to identify how
measures in a space interact with canonical families of sets in the space. In particular …
measures in a space interact with canonical families of sets in the space. In particular …
Density of continuous functions in Sobolev spaces with applications to capacity
S Eriksson-Bique, P Poggi-Corradini - arXiv preprint arXiv:2303.00649, 2023 - arxiv.org
We show that capacity can be computed with locally Lipschitz functions in locally complete
and separable metric spaces. Further, we show that if $(X, d,\mu) $ is a locally complete and …
and separable metric spaces. Further, we show that if $(X, d,\mu) $ is a locally complete and …
Carnot rectifiability and Alberti representations
This paper introduces and studies the analogue of the notion of Lipschitz differentiability
space by Cheeger, using Carnot groups and Pansu derivatives as models. We call such …
space by Cheeger, using Carnot groups and Pansu derivatives as models. We call such …