16 citations · 28 across the 22 of their papers we have counts for
6 papers · 1 filter
A Marstrand projection theorem for lines
Shengwen Gan
Fix integers . For , let be the orthogonal projection. For , define the map \[ π_V: A(1,n)\rightarrow A(1,V)\bigsq…
Restriction estimates for quadratic manifolds of arbitrary codimensions
Shengwen Gan, Larry Guth, Changkeun Oh
The restriction conjecture is one of the famous problems in harmonic analysis. There have been many methods developed in the study of the conjecture for the paraboloid. In this pap…
Exceptional set estimate through Brascamp-Lieb inequality
Shengwen Gan
Fix integers , and numbers satisfying . The problem of exceptional set estimate is to determine \[T(a,s):=\sup_{A\subset \mathbb{R}^n\ \text{dim}A=…
Hausdorff dimension of unions of -planes
Shengwen Gan
We prove a conjecture of Héra on the dimension of unions of -planes. Let be integers, and . If , with $\text{dim}(\mathcal{…
Small cap square function estimates
Shengwen Gan
We introduce small cap square function estimates for parabola and cone, and prove the sharp estimates. More precisely, we study the inequalities of form \[ \|f\|_p\le C_{α,p}(R) \B…
Exceptional set estimates in finite fields
Paige Bright, Shengwen Gan
We study the exceptional set estimate for projections in . For each , let be the projection map. We…