Ivan Yuri Violo

works on

geometric analysis 1 isocapacitary inequality 1 mean curvature 1 metric measure spaces 1 RCD spaces 1 willmore inequality 1

From the 1 of 10 linked papers with an AI index.

activity

20242026

collaborators

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math.MG2026

On various Carleson-type geometric lemmas and uniform rectifiability in metric spaces: Part 2

Katrin FÃ¤ssler, Ivan Yuri Violo

We characterize uniform $k$ -rectifiability in Euclidean spaces in terms of a Carleson-type geometric lemma for a new notion of flatness coefficients, which we call $I^^{1}$ -numbers. Th…

math.MG2025

Second-order estimates for the $p$ -Laplacian in RCD spaces

Luca Benatti, Ivan Yuri Violo

We establish quantitative second-order Sobolev regularity for functions having a $2$ -integrable $p$ -Laplacian in bounded RCD spaces, with $p$ in a suitable range. In the finite-dim…

math.MG2025

On various Carleson-type geometric lemmas and uniform rectifiability in metric spaces: Part 1

Katrin FÃ¤ssler, Ivan Yuri Violo

We introduce new flatness coefficients, which we call $I^^{1}$ -numbers, for Ahlfors $k$ -regular sets in metric spaces ( $k \in N$ ). Using these coefficients for $k = 1$ , we charac…

math.MG2024

Notes on the Cheeger and Colding version of the Reifenberg theorem for metric spaces

Nicola Gigli, Ivan Yuri Violo

The classical Reifenberg's theorem says that a set which is sufficiently well approximated by planes uniformly at all scales is a topological HÃ¶lder manifold. Remarkably, this gen…

On various Carleson-type geometric lemmas and uniform rectifiability in metric spaces: Part 2

Second-order estimates for the p-Laplacian in RCD spaces

On various Carleson-type geometric lemmas and uniform rectifiability in metric spaces: Part 1

Notes on the Cheeger and Colding version of the Reifenberg theorem for metric spaces

Second-order estimates for the $p$ -Laplacian in RCD spaces