A nonlocal approximation of the area in codimension two

Abstract

For $s\in (0,1)$ we introduce a notion of fractional $s$-mass on $(n-2)$-dimensional closed, oriented surfaces in ${\mathbb{R}}^n$. Moreover, we prove its $\Gamma$-convergence, with respect to the flat topology, to the $(n-2)$-dimensional area, as $s$ tends to $1$.