Ivan Yuri Violo

activity

20212026

most citedTopological regularity of isoperimetric sets in PI spaces having a deformation property

7 citations · 10 across the 19 of their papers we have counts for

collaborators

19 papers

math.AP2026

Divergence-free concentrations come from vanishing sequences

Adolfo Arroyo-Rabasa, Francesco Nobili, Ivan Yuri Violo

A vanishing sequence $V_{n}$ of divergence-free matrix fields is one that is bounded in $L^{1}$ and is carried by open sets $A_{n}$ of vanishing volume. Recently established, Bouchitté's…

math.DG2026

Mean curvature and sharp Willmore inequalities in metric spaces

Nicola Gigli, Ivan Yuri Violo

The goal of this work is to introduce a notion of mean curvature for level sets of functions in non-smooth spaces with Ricci curvature bounded below, and to prove that it satisfies…

math.AP2026

Quantitative stability in distribution for the Sobolev inequality under curvature dimension condition

Max Fathi, Ivan Yuri Violo

The goal of this note is to investigate quantitative stability properties of the critical Sobolev inequality in $CD (N - 1, N)$ metric measure spaces. Assuming that the optimal c…

math.AP2025

Regularity for quasilinear elliptic equations in metric measure spaces

Simon Schulz, Ivan Yuri Violo

In the present article we prove second-order and Lipschitz regularity for quasilinear elliptic equations in metric spaces endowed with a lower bound on the Ricci curvature. The est…

math.AP2025

Generalized existence of extremizers for the sharp $p$ -Sobolev inequality on Riemannian manifolds with nonnegative curvature

Francesco Nobili, Ivan Yuri Violo

We study the generalized existence of extremizers for the sharp $p$ -Sobolev inequality on noncompact Riemannian manifolds in connection with nonnegative curvature and Euclidean vol…

math.MG2025

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

Katrin Fässler, 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 $ι$ -numbers. The…

math.AP2025

An overview of regularity results for the Laplacian and $p$ -Laplacian in metric spaces

Ivan Yuri Violo

We review some regularity results for the Laplacian and $p$ -Laplacian in metric measure spaces. The focus is mainly on interior Hölder, Lipschitz and second-regularity estimates an…

math.AP2024

Fine Pólya-Szegő rearrangement inequalities in metric spaces and applications

Francesco Nobili, Ivan Yuri Violo

We study fine Pólya-Szegő rearrangement inequalities into weighted intervals for Sobolev functions and functions of bounded variation defined on metric measure spaces supporting an…

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 Hölder manifold. Remarkably, this gene…

math.MG2024★ 1 cited

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.MG2023

Ricci curvature bounded below and uniform rectifiability

Matthew Hyde, Michele Villa, Ivan Yuri Violo

We prove that Ahlfors-regular RCD spaces are uniformly rectifiable. The same is shown for Ahlfors regular boundaries of non-collapsed RCD spaces. As an application we deduce a type…

math.MG2023

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

Katrin Fässler, Ivan Yuri Violo

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

math.SP2023

Pleijel nodal domain theorem in non-smooth setting

Nicolò De Ponti, Sara Farinelli, Ivan Yuri Violo

We prove the Pleijel theorem in non-collapsed RCD spaces, providing an asymptotic upper bound on the number of nodal domains of Laplacian eigenfunctions. As a consequence, we obtai…

math.MG2023

Fat triangles inscribed in arbitrary planar domains

Ivan Yuri Violo

In 1964 A. Bruckner observed that any bounded open set in the plane has an inscribed triangle, that is a triangle contained in the open set and with the vertices lying on the bound…

math.MG2023★ 7 cited

Topological regularity of isoperimetric sets in PI spaces having a deformation property

Gioacchino Antonelli, Enrico Pasqualetto, Marco Pozzetta +1

We prove topological regularity results for isoperimetric sets in PI spaces having a suitable deformation property, which prescribes a control on the increment of the perimeter of…

math.DG2022

Stability of Sobolev inequalities on Riemannian manifolds with Ricci curvature lower bounds

Francesco Nobili, Ivan Yuri Violo

We study the qualitative stability of two classes of Sobolev inequalities on Riemannian manifolds. In the case of positive Ricci curvature, we prove that an almost extremal functio…

math.DG2021

Rigidity and almost rigidity of Sobolev inequalities on compact spaces with lower Ricci curvature bounds

Francesco Nobili, Ivan Yuri Violo

We prove that if $M$ is a closed $n$ -dimensional Riemannian manifold, $n \geq 3$ , with $Ric \geq n - 1$ and for which the optimal constant in the critical Sobolev inequality equal…

math.MG2021

A remark on two notions of flatness for sets in the Euclidean space

Ivan Yuri Violo

In this note we compare two ways of measuring the $n$ -dimensional "flatness" of a set $S \subset R^{d}$ , where $n \in N$ and $d > n$ . The first one is to consider the c…

math.DG2021★ 2 cited

Monotonicity formulas for harmonic functions in $RCD (0, N)$ spaces

Nicola Gigli, Ivan Yuri Violo

We generalize to the $RCD (0, N)$ setting a family of monotonicity formulas by Colding and Minicozzi for positive harmonic functions in Riemannian manifolds with non-negative R…

Divergence-free concentrations come from vanishing sequences

Mean curvature and sharp Willmore inequalities in metric spaces

Quantitative stability in distribution for the Sobolev inequality under curvature dimension condition

Regularity for quasilinear elliptic equations in metric measure spaces

Generalized existence of extremizers for the sharp p-Sobolev inequality on Riemannian manifolds with nonnegative curvature

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

An overview of regularity results for the Laplacian and p-Laplacian in metric spaces

Fine Pólya-Szegő rearrangement inequalities in metric spaces and applications

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

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

Ricci curvature bounded below and uniform rectifiability

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

Pleijel nodal domain theorem in non-smooth setting

Fat triangles inscribed in arbitrary planar domains

Topological regularity of isoperimetric sets in PI spaces having a deformation property

Stability of Sobolev inequalities on Riemannian manifolds with Ricci curvature lower bounds

Rigidity and almost rigidity of Sobolev inequalities on compact spaces with lower Ricci curvature bounds

A remark on two notions of flatness for sets in the Euclidean space

Monotonicity formulas for harmonic functions in RCD(0,N) spaces

Generalized existence of extremizers for the sharp $p$ -Sobolev inequality on Riemannian manifolds with nonnegative curvature

An overview of regularity results for the Laplacian and $p$ -Laplacian in metric spaces

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

Monotonicity formulas for harmonic functions in $RCD (0, N)$ spaces