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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…
math.MG2025
On various Carleson-type geometric lemmas and uniform rectifiability in metric spaces: Part 2
Katrin Fässler, Ivan Yuri Violo
We characterize uniform -rectifiability in Euclidean spaces in terms of a Carleson-type geometric lemma for a new notion of flatness coefficients, which we call -numbers. The…
math.MG2023
On various Carleson-type geometric lemmas and uniform rectifiability in metric spaces: Part 1
Katrin Fässler, Ivan Yuri Violo
We introduce new flatness coefficients, which we call -numbers, for Ahlfors -regular sets in metric spaces (). Using these coefficients for , we charact…