Mattia Freguglia

activity

20222026

collaborators

8 papers

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.AP2025

$Γ$ -convergence for higher order nonlocal phase transitions

Hardy Chan, Serena Dipierro, Mattia Freguglia +2

For every $0 < s < 3/4$ , we study the asymptotic behavior of the $ε$ -rescaled sum of the $s$ -fractional Allen-Cahn energy and the squared $L^{2}$ -norm of its first variation…

math.DG2025

Min-max theory and Yamabe metrics on conical four-manifolds

Mattia Freguglia, Andrea Malchiodi, Francesco Malizia

We prove existence of Yamabe metrics on four-manifolds possessing finitely-many conical points with $Z_{2}$ -group, using for the first time a min-max scheme in the singular…

math.AP2025

Coercivity and Gamma-convergence of the $p$ -energy of sphere-valued Sobolev maps

Michele Caselli, Mattia Freguglia, Nicola Picenni

We consider sequences of maps from an $(n + m)$ -dimensional domain into the $(n - 1)$ -sphere, which satisfy a natural $p$ -energy growth, as $p$ approaches $n$ from below. We prove that…

math.AP2024

$Γ$ -Limsup estimate for a nonlocal approximation of the Willmore functional

Hardy Chan, Mattia Freguglia, Marco Inversi

We propose a possible nonlocal approximation of the Willmore functional, in the sense of Gamma-convergence, based on the first variation ot the fractional Allen-Cahn energies, and…

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.DG2024

Yamabe metrics on conical manifolds

Mattia Freguglia, Andrea Malchiodi

We prove existence of Yamabe metrics on singular manifolds with conical points and conical links of Einstein type that include orbifold structures. We deal with metrics of generic…

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 […

Another look at a notion of fractional mass in codimension two

Γ-convergence for higher order nonlocal phase transitions

Min-max theory and Yamabe metrics on conical four-manifolds

Coercivity and Gamma-convergence of the p-energy of sphere-valued Sobolev maps

Γ-Limsup estimate for a nonlocal approximation of the Willmore functional

A nonlocal approximation of the area in codimension two

Yamabe metrics on conical manifolds

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

$Γ$ -convergence for higher order nonlocal phase transitions

Coercivity and Gamma-convergence of the $p$ -energy of sphere-valued Sobolev maps

$Γ$ -Limsup estimate for a nonlocal approximation of the Willmore functional