Tainara Borges

Falconer-type problems seek Hausdorff-dimension thresholds guaranteeing that thin subsets of R d contain rich geometric patterns. For a compact set E ⊂ R d , the classical object is the distance set ∆(E) = { |x − y| : x, y ∈ E }, and its pinned...

Given a compact set E ⊂ R^d , its distance set is ∆(E) = { |x − y| : x, y ∈ E }, and for y ∈ E, the pinned distance set of E at y is ∆ y (E) = { |x − y| : x ∈ E }. A classical result of Mattila and Sjölin shows that the unpinned distance set ∆(E) has...