Author

Ivan Yuri Violo

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Preprint Jul 2026

Mean curvature and sharp Willmore inequalities in metric spaces

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 sharp geometric inequalities. More precisely, we define a suitable Willmore functional $\mathcal{W}$ on Sobolev functions, whose domain of...

Nicola Gigli, Ivan Yuri Violo · 1 citation

Preprint Jul 2026

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

The goal of this note is to investigate quantitative stability properties of the critical Sobolev inequality in ${\sf CD}(N-1,N)$ metric measure spaces. Assuming that the optimal constant for the inequality is almost the same as the one of the round sphere, we show that the cumulative distribution of any almost extrema...

Max Fathi, Ivan Yuri Violo · 0 citations