Yumeng Ou

activity

20232026

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5 papers · 1 filter

math.CA2026

From weighted paraboloid restriction to $k$ -stars and distance graphs

Tainara Borges, Yumeng Ou, Marcus Pasquariello

In this paper, we study pinned $k$ -star distance sets associated to compact subsets of $R^{n}$ , $n \geq 2$ . For pins $x_{1}, \dots, x_{k} \in E$ , the pinned $k$ -star distance set is…

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 $G = (V, E)$ , with vertex set $V$ and edge set $E$ , how large the…

math.CA2025

Nonempty interior of pinned distance and tree sets

Tainara Borges, Benjamin Foster, Yumeng Ou +1

For a compact set $E \subset R^{d}$ , $d \geq 2$ , consider the pinned distance set $Δ^{y} (E) = {∣ x - y ∣ : x \in E}$ . Peres and Schlag showed that if the Hausdorff dimens…

math.CA2023

Sobolev smoothing estimates for bilinear maximal operators with fractal dilation sets

Tainara Borges, Benjamin Foster, Yumeng Ou

Given a hypersurface $S \subset R^{2 d}$ , we study the bilinear averaging operator that averages a pair of functions over $S$ , as well as more general bilinear multipliers o…

From weighted paraboloid restriction to k-stars and distance graphs

On volume vectors determined by hypergraphs in thin subsets of Euclidean space

Falconer-type results for any finite graph with multiple pins

Nonempty interior of pinned distance and tree sets

Sobolev smoothing estimates for bilinear maximal operators with fractal dilation sets

From weighted paraboloid restriction to $k$ -stars and distance graphs