8 papers
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 local smoothing estimates for wave equations
Shengwen Gan, Danqing He, Xiaochun Li +1
We prove sharp local smoothing estimates for wave equations on compact Riemannian manifolds in dimensions for odd and obtain improved estimates in even dimensions. This i…
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…