From the 1 of 6 linked papers with an AI index.
6 papers
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…
From weighted paraboloid restriction to -stars and distance graphs
Tainara Borges, Yumeng Ou, Marcus Pasquariello
In this paper, we study pinned -star distance sets associated to compact subsets of , . For pins , the pinned -star distance set is…
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…
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…
Restriction and Kakeya maximal estimates in
Tainara Borges, Tiklung Chan, Mingfeng Chen +3
By combining the planebrush argument of Katz and Zahl \cite{katz21} with the decoupling-incidence method of Wang and Wu \cite{WangWu2024}, we derive new bounds for the Fourier rest…
Study guide for "On restricted projections to planes in "
Tainara Borges, Siddharth Mulherkar, Tongou Yang
This article is a study guide for ``On restricted projections to planes in " [arXiv:2207.13844] by Gan, Guo, Guth, Harris, Maldague and Wang. We first present the main…