geometric measure theory 1Hausdorff dimension 1nonempty interior 1pinned distance sets 1tree configurations 1
From the 1 of 3 linked papers with an AI index.
3 papers
math.CA2026
Nonempty interior of pinned distance and tree sets
Tainara Borges, Benjamin Foster, Yumeng Ou +1
The authors establish new dimensional thresholds under which a compact set in the plane has a point whose pinned distance set contains an interval, improving previous results and e…
math.CA2026
On volume vectors determined by hypergraphs in thin subsets of Euclidean space
Tainara Borges, Ben Foster, Yumeng Ou +2
Generalizing the Falconer distance problem, the authors of this paper recently established the first non-trivial dimensional threshold for any distance graph in high enough of a di…
math.CA2026
Falconer-type results for any finite graph with multiple pins
Tainara Borges, Ben Foster, Yumeng Ou +2
A generalization of the celebrated Falconer distance problem asks for a graph , with vertex set and edge set , how large the…