7 papers · 1 filter
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_…
Decoupling for AD-regular sets on the parabola
Ciprian Demeter, Yuqiu Fu
We improve the decoupling exponent for functions with spectrum inside AD-regular collections of arcs on the parabola. We achieve this by incorporating recent Szemerédi--Trotter-ty…
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…
Incidence estimates for quasi-product sets and applications
Ciprian Demeter, William O'Regan
We use recent advances in the theory of Furstenberg sets to prove new incidence results of Szemerédi--Trotter strength for -discretized structures with Cartesian product flavo…
Level set estimates for the periodic Schrödinger maximal function on
Ciprian Demeter
We prove (essentially) sharp level set estimates for the periodic Schrödinger maximal operator in a certain range of the cut-off parameter.
Szemerédi-Trotter bounds for tubes and applications
Ciprian Demeter, Hong Wang
We prove sharp estimates for incidences involving planar tubes that satisfy packing conditions. We apply them to improve the estimates for the Fourier transform of fractal measures…