Characterising the big pieces of Lipschitz graphs property using projections

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Martikainen , H & Orponen , T 2018 , ' Characterising the big pieces of Lipschitz graphs property using projections ' , European Mathematical Society. Journal , vol. 20 , no. 5 , pp. 1055-1073 . https://doi.org/10.4171/JEMS/782

Title: Characterising the big pieces of Lipschitz graphs property using projections
Author: Martikainen, Henri; Orponen, Tuomas
Contributor: University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Department of Mathematics and Statistics
Date: 2018
Language: eng
Number of pages: 19
Belongs to series: European Mathematical Society. Journal
ISSN: 1435-9855
URI: http://hdl.handle.net/10138/307144
Abstract: We characterise the big pieces of Lipschitz graphs property in terms of projections. Roughly speaking, we prove that if a large subset of an n-Ahlfors-David regular set E subset of R-d has plenty of projections in L-2, then a large part of E is contained in a single Lipschitz graph. This is closely related to a question of G. David and S. Semmes.
Subject: Projections
Lipschitz graphs
big pieces of sets
uniform rectifiability
111 Mathematics
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