7 papers · 1 filter
Lebesgue measure of distance sets and ball inflation
Shengwen Gan, Bochen Liu, Shukun Wu
We give an alternative proof of the result of Guth-Iosevich-Ou-Wang on the Falconer distance conjecture: if a compact set in the plane has Hausdorff dimension , the…
Near optimal three-fold additive energy bound for points on convex curves
Adam Cushman, Ciprian Demeter, Shukun Wu
Let be finite and let , where is strictly convex. We show that \[ J_3(γ(X)) =\#\{(x_1,\ldots,x_6)\in X^6:\sum_{i=1}^3γ(x_i)=\sum_{i=4}^6γ(x_…
Sharp microlocal Kakeya--Nikodym estimates for eigenfunctions with applications
Chuanwei Gao, Shukun Wu, Yakun Xi
We extend the microlocal Kakeya--Nikodym bounds for eigenfunctions of Blair--Sogge to a larger range of exponents, which is optimal in all dimensions on general manifolds.…
Restriction and decoupling estimates for the hyperbolic paraboloid in
Ciprian Demeter, Shukun Wu
We prove bilinear -decoupling and refined bilinear decoupling inequalities for the truncated hyperbolic paraboloid in . As an application, we prove the associ…
On almost everywhere convergence of planar Bochner-Riesz means
Xiaochun Li, Shukun Wu
We demonstrate the almost everywhere convergence of the planar Bochner-Riesz means for functions in the optimal range when . This is achieved by establishing…
A study guide for "On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane" after T. Orponen and P. Shmerkin
Jacob B. Fiedler, Guo-Dong Hong, Donggeun Ryou +1
This article is a study guide for ``On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane" by Orponen and Shmerkin. We begin by introducing Fursten…
A weighted decoupling inequality and its application to the maximal Bochner-Riesz problem
Shengwen Gan, Shukun Wu
We prove some weighted -decoupling estimates when . As an application, we give a result beyond the real interpolation exponents for the maximal Bochner-Riesz…