5 papers
A geometric approach to Poincaré inequality and Minkowski content of separating sets
Emanuele Caputo, Nicola Cavallucci
The goal of this paper is to continue the study of the relation between the Poincaré inequality and the lower bounds of Minkowski content of separating sets, initiated in our previ…
Poincaré inequality and energy of separating sets
Emanuele Caputo, Nicola Cavallucci
We study geometric characterizations of the Poincaré inequality in doubling metric measure spaces in terms of properties of separating sets. Given a couple of points and a set sepa…
GH-convergence of CAT-spaces: stability of the Euclidean factor
Nicola Cavallucci
We prove that if a sequence of geodesically complete CAT-spaces with uniformly cocompact discrete groups of isometries converges in the Gromov-Hausdorff sense to $X_\inf…
A GH-compactification of CAT-groups via totally disconnected, unimodular actions
Nicola Cavallucci
We give a detailed description of the possible limits in the equivariant-Gromov-Hausdorff sense of sequences , where the 's are proper, geodesically complete, unifo…
The -completion of the space of Riemannian metrics is CAT: a shorter proof
Nicola Cavallucci
We reprove in an easier way a result of Brian Clarke: the completion of the space of Riemannian metrics of a compact, orientable smooth manifold with respect to the -distance…