7 papers
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…
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…
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…
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-Ãmery Ricci curvature bounded from below. We rigorously…
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…
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…