Download this article
 Download this article For screen
For printing
Recent Issues

Volume 17
Issue 5, 1501–1870
Issue 4, 1127–1500
Issue 3, 757–1126
Issue 2, 379–756
Issue 1, 1–377

Volume 16, 10 issues

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
 
Author index
To appear
 
Other MSP journals
Structure of sets with nearly maximal Favard length

Alan Chang, Damian Dąbrowski, Tuomas Orponen and Michele Villa

Vol. 17 (2024), No. 4, 1473–1500
Abstract

Let E B(1) 2 be an 1 measurable set with 1(E) < , and let L 2 be a line segment with 1(L) = 1(E). It is not hard to see that Fav (E) Fav (L). We prove that in the case of near equality, that is,

Fav (E) Fav (L) δ,

the set E can be covered by an 𝜖-Lipschitz graph, up to a set of length 𝜖. The dependence between 𝜖 and δ is polynomial: in fact, the conclusions hold with 𝜖 = Cδ170 for an absolute constant C > 0.

Keywords
Favard length, Besicovitch projection theorem, Lipschitz graph
Mathematical Subject Classification
Primary: 28A75
Secondary: 28A78
Milestones
Received: 7 April 2022
Revised: 6 August 2022
Accepted: 27 October 2022
Published: 17 May 2024
Authors
Alan Chang
Department of Mathematics
Washington University in St. Louis
MO
United States
Damian Dąbrowski
Department of Mathematics and Statistics
University of Jyväskylä
Finland
Tuomas Orponen
Department of Mathematics and Statistics
University of Jyväskylä
Finland
Michele Villa
Research Unit of Mathematical Sciences
University of Oulu
Finland

Open Access made possible by participating institutions via Subscribe to Open.