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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…
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…