Structure of sets with nearly maximal Favard length
Chang, A., Dąbrowski, D., Orponen, T., & Villa, M. (2024). Structure of sets with nearly maximal Favard length. Analysis and PDE, 17(4), 1473-1500. https://doi.org/10.2140/apde.2024.17.1473
Published in
Analysis and PDEDate
2024Copyright
© 2024 MSP (Mathematical Sciences Publishers)
Let E⊂B(1)⊂R2 be an H1 measurable set with H1(E)<∞, and let L⊂R2 be a line segment with H1(L)=H1(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=Cδ1∕70 for an absolute constant C>0.
Publisher
Mathematical Sciences PublishersISSN Search the Publication Forum
2157-5045Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/215874980
Metadata
Show full item recordCollections
Additional information about funding
Dabrowski and Orponen are supported by the Academy of Finland via the project Incidences on Fractals, grant 321896. Orponen is also supported by the Academy of Finland via the project Quantitative rectifiability in Euclidean and non-Euclidean spaces, grants 309365, 314172. Villa was supported by a starting grant of the University of Oulu.License
Except where otherwise noted, this item's license is described as CC BY 4.0