3 papers
math.AP2026
A new Duhamel-type principle with applications to geometric (in)equalities
Michele Caselli, Luca Gennaioli
We introduce a simple new method, based on the Caffarelli-Silvestre extension and a Duhamel-type formula, to derive exact pointwise identities for fractional commutators and nonlin…
math.DG2025
Yau's conjecture for nonlocal minimal surfaces
Michele Caselli, Enric Florit-Simon, Joaquim Serra
We introduce nonlocal minimal surfaces on closed manifolds and establish a far-reaching Yau-type result: in every closed, -dimensional Riemannian manifold we construct infinitel…
math.AP2025
Fractional Sobolev spaces on Riemannian manifolds
Michele Caselli, Enric Florit-Simon, Joaquim Serra
This article studies the canonical Hilbert energy on a Riemannian manifold for , with particular focus on the case of closed manifolds. Several equivalent d…