activity
20242026
collaborators

7 papers

math.DG2026

Ollivier--Ricci Curvature on Groups of Polynomial Growth

Camillo Brena, Elia Bruè

We study Ollivier--Ricci curvature on Cayley graphs of groups of polynomial growth. Our main result shows that non-negative Ollivier--Ricci curvature forces the group to be virtual…

math.FA2025

Maps of bounded variation from PI spaces to metric spaces

Camillo Brena, Francesco Nobili, Enrico Pasqualetto

We study maps of bounded variation defined on a metric measure space and valued into a metric space. Assuming the source space to satisfy a doubling and Poincaré property, we prod…

math.DG2025

Instability of the fundamental group for non-collapsed Ricci-limits

Camillo Brena

We construct two sequences of closed -dimensional manifolds with non-negative Ricci curvature, diameter bounded from above by , and volume bounded from below by , with d…

math.DG2025

Perelman's entropy and heat kernel bounds on RCD spaces

Camillo Brena

We study Perelman's W-entropy functional on finite-dimensional RCD spaces, a synthetic generalization of spaces with Bakry-Émery Ricci curvature bounded from below. We rigorously…

math.AP2025

Remarks and Conjectures on Stationary Varifolds

Camillo Brena, Stefano Decio, Camillo De Lellis

In this paper, we revisit some known results about stationary varifolds using simpler arguments. In particular, we obtain the height bound and the Lipschitz approximation along wit…

math.AP2025

rectifiability of stationary varifolds

Camillo Brena, Camillo De Lellis, Federico Franceschini

In this paper we prove that, for every integers and , the support of any stationary -dimensional integer rectifiable varifold in an open set $U\subset \ma…