Nicola Picenni

activity

20172026

most citedOptimal constants for a non-local approximation of Sobolev norms and total variation

7 citations · 15 across the 14 of their papers we have counts for

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math.DG2026

Another look at a notion of fractional mass in codimension two

Michele Caselli, Mattia Freguglia, Nicola Picenni

We study a notion of fractional $s$ -mass for codimension-two currents on closed Riemannian manifolds, defined via energy minimization with a prescribed Jacobian constraint. We prov…

math.DG2024

A nonlocal approximation of the area in codimension two

Michele Caselli, Mattia Freguglia, Nicola Picenni

For $s \in (0, 1)$ we introduce a notion of fractional $s$ -mass on $(n - 2)$ -dimensional closed, orientable surfaces in $R^{n}$ . Moreover, we prove its $Γ$ -convergence, with respect to…

math.DG2022

On a conjecture of De Giorgi about the phase-field approximation of the Willmore functional

Giovanni Bellettini, Mattia Freguglia, Nicola Picenni

In 1991 De Giorgi conjectured that, given $λ > 0$ , if $μ_{ε}$ stands for the density of the Allen-Cahn energy and $v_{ε}$ represents its first variation, then $\int […