L. Guth

activity

20052026

most citedOn the Erdos distinct distance problem in the plane

105 citations · 592 across the 57 of their papers we have counts for

collaborators

64 papers

math.CA2026

Curved Kakeya problems and the projective geometry of paths

Shaoming Guo, Larry Guth, Arian Nadjimzadah +2

We introduce a general framework for curved Kakeya problems in $R^{n}$ , encompassing those arising from Hörmander-type oscillatory integrals. Every family of curves determin…

math.CA2023

A sharp square function estimate for the moment curve in $R^{n}$

Larry Guth, Dominique Maldague

We use high-low frequency methods developed in the context of decoupling to prove sharp (up to $C_{ε} R^{ε}$ ) square function estimates for the moment curve $(t, t^{2}, \dots, t^{n})$ in $\ma…

math.CA2023

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…

math.CA2023★ 1 cited

Small cap decoupling for the paraboloid in $R^{n}$

Larry Guth, Dominique Maldague, Changkeun Oh

We extend the small cap decoupling program established by Demeter, Guth, and Want to paraboloids in $R^{n}$ for some range of $p$ .

math.CA2022★ 2 cited

An exceptional set estimate for restricted projections to lines in $R^{3}$

Shengwen Gan, Larry Guth, Dominique Maldague

Let $γ : [0, 1] \to S^{2}$ be a non-degenerate curve in $R^{3}$ , that is to say, $det (γ (θ), γ^{'} (θ), γ^{''} (θ)) \neq = 0$ . For each $θ \in [0, 1]$ , let $l_θ=\{tγ(θ)…

math.CA2022★ 3 cited

On restricted projections to planes in $R^{3}$

Shengwen Gan, Shaoming Guo, Larry Guth +3

Let $γ : [0, 1] \to S^{2}$ be a non-degenerate curve in $R^{3}$ , that is to say, $det (γ (θ), γ^{'} (θ), γ " (θ)) \neq = 0$ . For each $θ \in [0, 1]$ , let $V_θ=γ(θ)^\pe…

Curved Kakeya problems and the projective geometry of paths

A sharp square function estimate for the moment curve in Rn

Restriction estimates for quadratic manifolds of arbitrary codimensions

Small cap decoupling for the paraboloid in Rn

An exceptional set estimate for restricted projections to lines in R3

On restricted projections to planes in R3

A sharp square function estimate for the moment curve in $R^{n}$

Small cap decoupling for the paraboloid in $R^{n}$

An exceptional set estimate for restricted projections to lines in $R^{3}$

On restricted projections to planes in $R^{3}$