3 papers
math.AP2025
The $\eps-\eps^β$ property for clusters with double density
A. Pratelli, V. Scattaglia
This article is devoted to extend the "$\eps-\eps^β$ property" to the case of clusters in an Euclidean space with a double density.
math.AP2025
Particle approximation of nonlocal interaction energies
Davide Carazzato, Aldo Pratelli, Ihsan Topaloglu
We consider Riesz-type nonlocal energies with general interaction kernels and their discretizations related to particle systems. We prove that the discretized energies -converge…
math.FA2025
Connectedness properties of small minimal clusters in Riemannian or Finsler manifolds
Stefano Nardulli, Aldo Pratelli
We prove that in a compact Riemannian manifold, the -minimal clusters of sufficiently small total volume are connected and with small diameter, while in a more general Finsler m…