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

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Showing 2021Show all

3 papers · 1 filter

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…

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

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