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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…
math.MG2023
Sobolev, BV and perimeter extensions in metric measure spaces
Emanuele Caputo, Jesse Koivu, Tapio Rajala
We study extensions of sets and functions in general metric measure spaces. We show that an open set has the strong BV extension property if and only if it has the strong extension…