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math.DG2022
A characterization of gauge balls in by horizontal curvature
Chiara Guidi, Vittorio Martino, Giulio Tralli
In this paper we aim at identifying the level sets of the gauge norm in the Heisenberg group via the prescription of their (non-constant) horizontal mean curvature.…
math.AP2022
A universal heat semigroup characterisation of Sobolev and BV spaces in Carnot groups
Nicola Garofalo, Giulio Tralli
In sub-Riemannian geometry there exist, in general, no known explicit representations of the heat kernels, and these functions fail to have any symmetry whatsoever. In particular,…