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• Plenty of big projections imply big pieces of Lipschitz graphs 

  Orponen, Tuomas (Springer, 2021)

  I prove that closed n-regular sets E⊂Rd with plenty of big projections have big pieces of Lipschitz graphs. In particular, these sets are uniformly n-rectifiable. This answers a question of David and Semmes from 1993.

• Extensions and corona decompositions of low-dimensional intrinsic Lipschitz graphs in Heisenberg groups 

  Di Donato, Daniela; Fässler, Katrin (Springer, 2022)

  This note concerns low-dimensional intrinsic Lipschitz graphs, in the sense of Franchi, Serapioni, and Serra Cassano, in the Heisenberg group Hn, n∈N. For 1⩽k⩽n, we show that every intrinsic L-Lipschitz graph over a subset ...

• Intrinsic Lipschitz graphs and vertical β-numbers in the Heisenberg group 

  Chousionis, Vasileios; Fässler, Katrin; Orponen, Tuomas (Johns Hopkins University Press, 2019)

  The purpose of this paper is to introduce and study some basic concepts of quantitative rectifiability in the first Heisenberg group H. In particular, we aim to demonstrate that new phenomena arise compared to the Euclidean ...

• Lipschitz Carnot-Carathéodory Structures and their Limits 

  Antonelli, Gioacchino; Le Donne, Enrico; Nicolussi Golo, Sebastiano (Springer Science and Business Media LLC, 2023)

  In this paper we discuss the convergence of distances associated to converging structures of Lipschitz vector fields and continuously varying norms on a smooth manifold. We prove that, under a mild controllability assumption ...

• Semmes surfaces and intrinsic Lipschitz graphs in the Heisenberg group 

  Fässler, Katrin; Orponen, Tuomas; Rigot, Séverine (American Mathematical Society, 2020)

  A Semmes surface in the Heisenberg group is a closed set $ S$ that is upper Ahlfors-regular with codimension one and satisfies the following condition, referred to as Condition B. Every ball $ B(x,r)$ with $ x \in S$ and ...