3 papers
math.DG2024
On the dimension of the singular set of perimeter minimizers in spaces with a two-sided Ricci curvature bound
Alessandro Cucinotta, Francesco Fiorani
We show that the Hausdorff dimension of the singular set of perimeter minimizers in non-collapsed Ricci limit spaces with a two-sided Ricci curvature bound is at most , where…
math.DG2023
Monotonicity formula and stratification of the singular set of perimeter minimizers in RCD spaces
Francesco Fiorani, Andrea Mondino, Daniele Semola
The goal of this paper is to establish a monotonicity formula for perimeter minimizing sets in RCD(0,N) metric measure cones, together with the associated rigidity statement. The a…
math.AP2021
On the validity of the tight-binding method for describing systems of subwavelength resonators
Habib Ammari, Francesco Fiorani, Erik Orvehed Hiltunen
The goal of this paper is to relate the capacitance matrix formalism to the tight-binding approximation. By doing so, we open the way to the use of mathematical techniques and tool…