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Sobolev spaces via chains in metric measure spaces
Emanuele Caputo, Nicola Cavallucci
We define the chain Sobolev space on a possibly non-complete metric measure space in terms of chain upper gradients. In this context, -chains are a finite collection o…
math.MG2024
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…
math.MG2024
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…