Rademacherin lause
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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 ... -
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 ... -
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 ... -
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 ...