Plenty of big projections imply big pieces of Lipschitz graphs
Orponen, T. (2021). Plenty of big projections imply big pieces of Lipschitz graphs. Inventiones Mathematicae, 226(2), 653-709. https://doi.org/10.1007/s00222-021-01055-z
Published inInventiones Mathematicae
© The Author(s) 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.
Publication in research information system
MetadataShow full item record
Additional information about fundingOpen access funding provided by University of Jyväskylä (JYU).
Showing items with similar title or keywords.
Extensions and corona decompositions of low-dimensional intrinsic Lipschitz graphs in Heisenberg groups Di Donato, Daniela; Fässler, Katrin (Springer, 2021)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 ...
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 ...
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 ...
Heinonen, Juha (University of Jyväskylä, 2005)
Bokrantz, Rasmus; Miettinen, Kaisa (American Association of Physicists in Medicine, 2015)Purpose: To eliminate or reduce the error to Pareto optimality that arises in Pareto surface navigation when the Pareto surface is approximated by a small number of plans. Methods: The authors propose to project the ...