A group-theoretic viewpoint on Erdös-Falconer problems and the Mattila integral

DOI10.4171/RMI/854zbMath1329.52015arXiv1306.3598OpenAlexW2963847013MaRDI QIDQ888920

Bochen Liu, Allan Greenleaf, Alexander Iosevich, Eyvindur Ari Palsson

Publication date: 3 November 2015

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.3598

zbMATH Keywords

Erdös-Falconer problemsMattila integral

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Erd?s problems and related topics of discrete geometry (52C10) Configuration theorems in linear incidence geometry (51A20)

Related Items (28)

Erdős type problems in modules over cyclic rings ⋮ Finite configurations in sparse sets ⋮ Configurations in fractals ⋮ Finite point configurations and the regular value theorem in a fractal setting ⋮ Rigidity, Graphs and Hausdorff Dimension ⋮ Discrete maximal operators over surfaces of higher codimension ⋮ A Mattila-Sjölin theorem for triangles ⋮ On some properties of sparse sets: a survey ⋮ Falconer type functions in three variables ⋮ Embedding bipartite distance graphs under Hamming metric in finite fields ⋮ Three Applications of the Siegel Mass Formula ⋮ Group actions, the Mattila integral and applications ⋮ Average decay of the Fourier transform of measures with applications ⋮ Existence of similar point configurations in thin subsets of \(\mathbb{R}^d\) ⋮ Erdös--Falconer Distance Problem under Hamming Metric in Vector Spaces over Finite Fields ⋮ An \(L^2\)-identity and pinned distance problem ⋮ Large sets avoiding patterns ⋮ Falconer distance problem, additive energy and Cartesian products ⋮ On sets containing an affine copy of bounded decreasing sequences ⋮ Dimensional lower bounds for Falconer type incidence theorems ⋮ Patterns in thick compact sets ⋮ Volumes spanned by \(k\)-point configurations in \(\mathbb{R}^d\) ⋮ Pinned distance problem, slicing measures, and local smoothing estimates ⋮ Improvement on 2-chains inside thin subsets of Euclidean spaces ⋮ DIMENSIONS OF TRIANGLE SETS ⋮ ON GILP’S GROUP-THEORETIC APPROACH TO FALCONER’S DISTANCE PROBLEM ⋮ Areas spanned by point configurations in the plane ⋮ Fourier dimension and avoidance of linear patterns

Cites Work

• Multiparameter Projection Theorems with Applications to Sums-Products and Finite Point Configurations in the Euclidean Setting
• On the Hausdorff dimensions of distance sets
• New Bounds for the Discrete Fourier Restriction to the Sphere in 4D and 5D
• Unnamed Item

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