The main result of the present article is a Rademacher-type theorem for intrinsic Lipschitz
graphs of codimension in sub-Riemannian Heisenberg groups. For the purpose of proving …

In their 1991 and 1993 foundational monographs, David and Semmes characterized uniform
rectifiability for subsets of Euclidean space in a multitude of geometric and analytic ways …

We prove that the L_4 norm of the vertical perimeter of any measurable subset of the 3-
dimensional Heisenberg group H is at most a universal constant multiple of the …

Rectifiable sets, measures, currents and varifolds are foundational concepts in geometric
measure theory. The last four decades have seen the emergence of a wealth of connections …

arXiv:2112.00540v3 [math.CA] 1 Mar 2022 Page 1 arXiv:2112.00540v3 [math.CA] 1 Mar
2022 RECTIFIABILITY; A SURVEY PERTTI MATTILA Abstract. This is a survey on …

We introduce new flatness coefficients, which we call\emph {$\iota $-numbers}, for Ahlfors
regular sets in metric spaces. We investigate the relation between Carleson-type geometric …

We prove that in the first Heisenberg group, unlike Euclidean spaces and higher
dimensional Heisenberg groups, the best possible exponent for the strong geometric lemma …

It is shown that vertical projections in the Heisenberg group of sets of dimension strictly
greater than 3 almost surely have positive area. The proof uses the point-plate incidence …

Plenty of big projections imply big pieces of Lipschitz graphs | Inventiones mathematicae Skip to
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We show that the β-numbers of intrinsic Lipschitz graphs of Heisenberg groups ℍ n are
locally Carleson integrable when n≥ 2. Our main bound uses a novel slicing argument to …