Equilateral triangles in subsets of \(\mathbb{R}^d\) of large Hausdorff dimension

DOI10.1007/s11856-019-1848-8zbMath1417.52023arXiv1603.01907OpenAlexW2964070647MaRDI QIDQ2421890

Bochen Liu, Alexander Iosevich

Publication date: 18 June 2019

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.01907

zbMATH Keywords

equilateral triangle

Mathematics Subject Classification ID

Length, area, volume, other geometric measure theory (28A75) Erd?s problems and related topics of discrete geometry (52C10) Hausdorff and packing measures (28A78)

Related Items (15)

Density theorems for anisotropic point configurations ⋮ Finite point configurations and the regular value theorem in a fractal setting ⋮ Discrete maximal operators over surfaces of higher codimension ⋮ A Mattila-Sjölin theorem for triangles ⋮ The density of sets containing large similar copies of finite sets ⋮ Finite point configurations in products of thick Cantor sets and a robust nonlinear Newhouse Gap Lemma ⋮ Falconer type functions in three variables ⋮ Embedding bipartite distance graphs under Hamming metric in finite fields ⋮ Sparse bounds for the bilinear spherical maximal function ⋮ Simplices in thin subsets of Euclidean spaces ⋮ On sets containing an affine copy of bounded decreasing sequences ⋮ Small sets containing any pattern ⋮ Patterns in thick compact sets ⋮ Large sets avoiding linear patterns ⋮ Reviews

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