16 citations · 28 across the 22 of their papers we have counts for
19 papers · 1 filter
Sharp rational points counting near nondegenerate curves in
Shengwen Gan, Shaoming Guo, Changkeun Oh
We establish sharp bounds for rational points near compact smooth nondegenerate curves in , for every . For a nondegenerate curve in …
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…
Kakeya problem and projection problem for -geodesics in Grassmannians
Shengwen Gan
The Kakeya problem in is about estimating the size of union of -planes; the projection problem in is about estimating the size of projection of a s…
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=…