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

Showing 2022Show all

7 papers · 1 filter

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…

math.MG2022★ 2 cited

Degrees of maps and multiscale geometry

Aleksandr Berdnikov, Larry Guth, Fedor Manin

We study the degree of an $L$ -Lipschitz map between Riemannian manifolds, proving new upper bounds and constructing new examples. For instance, if $X_{k}$ is the connected sum of $k$ …

math.CA2022★ 2 cited

Decoupling estimates in Fourier analysis

Larry Guth

Decoupling is a recent development in Fourier analysis, which has applications in harmonic analysis, PDE, and number theory. We survey some applications of decoupling and some of t…

math.DG2022

Systolic almost-rigidity modulo 2

Hannah Alpert, Alexey Balitskiy, Larry Guth

No power law systolic freedom is possible for the product of mod $2$ systoles of dimension $1$ and codimension $1$ . This means that any closed $n$ -dimensional Riemannian manifold $…

math.CA2022

Amplitude dependent wave envelope estimates for the cone in $R^{3}$

Dominique Maldague, Larry Guth

For functions $f$ with Fourier transform supported in the truncated cone, we bound superlevel sets ${x \in R^{3} : ∣ f (x) ∣ > α}$ using an $α$ -dependent version of the wave envelo…