Dominique Maldague

activity

20182025

most citedImproved decoupling for the parabola

7 citations · 10 across the 6 of their papers we have counts for

collaborators

9 papers

math.CO2025

Heilbronn's triangle problem in three dimensions

Dominique Maldague, Hong Wang, Dmitrii Zakharov

We show that among any $n$ points in the unit cube one can find a triangle of area at most $n^{- 2/3 - c}$ for some absolute constant $c > 0$ . This gives the first non-trivial upper bo…

math.CA2025

Tangency counting for well-spaced circles

Dominique Maldague, Alexander Ortiz

In the late 90's, Tom Wolff introduced the circle tangency counting problem in his expository article on the Kakeya conjecture. For collections of well-spaced circles, we break the…

math.CA2024

On the small cap decoupling for the moment curve in $R^{3}$

Dominique Maldague, Changkeun Oh

This paper proves sharp small cap decoupling estimates for the moment curve $M^{n} = {(t, t^{2}, \dots, t^{n}) : 0 \leq t \leq 1}$ in the remaining small cap parameter ranges for $\m…

math.CA2022

A sharp square function estimate for the moment curve in $R^{3}$

Dominique Maldague

We prove a sharp (up to $C_{ε} R^{ε}$ ) $L^{7}$ square function estimate for the moment curve in $R^{3}$ .

math.CA2022★ 2 cited

An exceptional set estimate for restricted projections to lines in $R^{3}$

Shengwen Gan, Larry Guth, Dominique Maldague

Let $γ : [0, 1] \to S^{2}$ be a non-degenerate curve in $R^{3}$ , that is to say, $det (γ (θ), γ^{'} (θ), γ^{''} (θ)) \neq = 0$ . For each $θ \in [0, 1]$ , let $l_θ=\{tγ(θ)…

math.CA2021★ 1 cited

Sharp superlevel set estimates for small cap decouplings of the parabola

Yuqiu Fu, Larry Guth, Dominique Maldague

We prove sharp bounds for the size of superlevel sets ${x \in R^{2} : ∣ f (x) ∣ > α}$ where $α > 0$ and $f : R^{2} \to C$ is a Schwartz function with Fourier transform s…

Heilbronn's triangle problem in three dimensions

Tangency counting for well-spaced circles

On the small cap decoupling for the moment curve in R3

A sharp square function estimate for the moment curve in R3

An exceptional set estimate for restricted projections to lines in R3

Sharp superlevel set estimates for small cap decouplings of the parabola

On the small cap decoupling for the moment curve in $R^{3}$

A sharp square function estimate for the moment curve in $R^{3}$

An exceptional set estimate for restricted projections to lines in $R^{3}$