S. Dipierro

On the Weyl tube formula for nonlocal perimeters

We study the asymptotic behaviour of the nonlocal perimeter of tubular neighbourhoods. For a closed $C^{1,1}$ submanifold of Euclidean space, we show that a suitable rescaling of the nonlocal perimeter of its tube converges to an explicit constant times the Hausdorff measure of the submanifold. The constant is the frac...