5 citations · 12 across the 19 of their papers we have counts for
22 papers
Improvement of the dimension bound for unweighted RCD spaces
Camillo Brena, Luca Gennaioli
We show that if is an space for some and , then it is also a (non-collapsed) space. In other words, unw…
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…
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-Émery Ricci curvature bounded from below. We rigorously j…
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…
Lower Ricci Curvature Bounds and the Orientability of Spaces
Camillo Brena, Elia Bruè, Alessandro Pigati
We study orientability in spaces with Ricci curvature bounded below. Building on the theory developed by Honda, we establish equivalent characterizations of orientability for Ricci…
Unique continuation for area minimizing currents
Camillo Brena, Stefano Decio
The main goal of this work is to prove an instance of the unique continuation principle for area minimizing integral currents. More precisely, consider an -dimensional area mini…
Fine representation of Hessian of convex functions and Ricci tensor on RCD spaces
Camillo Brena, Nicola Gigli
It is known that on spaces one can define a distributional Ricci tensor . Here we give a fine description of this object by showing that it admits the pol…
About the general chain rule for functions of bounded variation
Camillo Brena, Nicola Gigli
We give an alternative proof of the general chain rule for functions of bounded variation ([ADM90]), which allows to compute the distributional differential of , where $φ…
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 produ…
Nguyen's approach to Sobolev spaces in metric measure spaces with unique tangents
Camillo Brena, Andrea Pinamonti
We extend Nguyen's characterization of Sobolev spaces to the setting of PI-metric measure spaces such that at a.e. point the tangent space (in the Gromov-Hausdorff sense)…
Functions with bounded Hessian-Schatten variation: density, variational and extremality properties
Luigi Ambrosio, Camillo Brena, Sergio Conti
In this paper we analyze in detail a few questions related to the theory of functions with bounded -Hessian-Schatten total variation, which are relevant in connection with the t…
Sobolev and BV functions on spaces via the short-time behaviour of the heat kernel
Camillo Brena, Enrico Pasqualetto, Andrea Pinamonti
In the setting of finite-dimensional spaces, we characterize the -Sobolev spaces for and the space of functions of bounded variation in term…
Linear Inverse Problems with Hessian-Schatten Total Variation
Luigi Ambrosio, Shayan Aziznejad, Camillo Brena +1
In this paper, we characterize the class of extremal points of the unit ball of the Hessian-Schatten total variation (HTV) functional. The underlying motivation for our work stems…
Subgraphs of functions on spaces
Gioacchino Antonelli, Camillo Brena, Enrico Pasqualetto
In this work we extend classical results for subgraphs of functions of bounded variation in to the setting of , where $\m…
Local vector measures
Camillo Brena, Nicola Gigli
Consider a BV function on a Riemannian manifold. What is its differential? And what about the Hessian of a convex function? These questions have clear answers in terms of (co)vecto…
Calculus and fine properties of functions of bounded variation on RCD spaces
Camillo Brena, Nicola Gigli
We generalize the classical calculus rules satisfied by functions of bounded variation to the framework of RCD spaces. In the infinite dimensional setting we are able to define an…
The Rank-One Theorem on spaces
Gioacchino Antonelli, Camillo Brena, Enrico Pasqualetto
We extend Alberti's Rank-One Theorem to metric measure spaces.
Weakly non-collapsed RCD spaces are strongly non-collapsed
Camillo Brena, Nicola Gigli, Shouhei Honda +1
We prove that any weakly non-collapsed RCD space is actually non-collapsed, up to a renormalization of the measure. This confirms a conjecture raised by De Philippis and the second…
Stability of a class of action functionals depending on convex functions
Luigi Ambrosio, Camillo Brena
We study the stability of a class of action functionals induced by gradients of convex functions with respect to Mosco convergence, under mild assumptions on the underlying space.
BV and Sobolev homeomorphisms between metric measure spaces and the plane
Camillo Brena, Daniel Campbell
We show that given a homeomorphism where is a open subset of and is a open subset of a -Ahlfors regular metric measure space supporting…