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math.FA2026
Characterizations of Sobolev and BV functions on Carnot groups
Francesco Serra Cassano, Kilian Zambanini
We establish two characterizations of real-valued Sobolev and BV functions on Carnot groups. The first is obtained via a nonlocal approximation of the distributional horizontal gra…
math.MG2026
On low-dimensional uniform rectifiability in Heisenberg groups
Katrin Fässler, Andrea Pinamonti, Kilian Zambanini
Refining an earlier result due to Hahlomaa, we provide a new Carleson-type condition for -regular sets in the Heisenberg group to have big pieces of Lipschitz ima…