4 papers
Sharp local smoothing estimates for curve averages
Shengwen Gan, Dominique Maldague, Changkeun Oh
We prove sharp local smoothing estimates for curve averages in all dimensions. As a corollary, we prove the sharp boundedness of the helical maximal operator in $\mathbb{R}^4…
Heilbronn's triangle problem in three dimensions
Dominique Maldague, Hong Wang, Dmitrii Zakharov
We show that among any points in the unit cube one can find a triangle of area at most for some absolute constant . This gives the first non-trivial upper bo…
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…
On the small cap decoupling for the moment curve in
Dominique Maldague, Changkeun Oh
This paper proves sharp small cap decoupling estimates for the moment curve in the remaining small cap parameter ranges for $\m…