Zobrazeno 1 - 10
of 214
pro vyhledávání: '"Guth, Larry"'
Autor:
Guth, Larry, Maynard, James
We prove new bounds for how often Dirichlet polynomials can take large values. This gives improved estimates for a Dirichlet polynomial of length $N$ taking values of size close to $N^{3/4}$, which is the critical situation for several estimates in a
Externí odkaz:
http://arxiv.org/abs/2405.20552
We identify a new way to divide the $\delta$-neighborhood of surfaces $\mathcal{M}\subset\mathbb{R}^3$ into a finitely-overlapping collection of rectangular boxes $S$. We obtain a sharp $(l^2,L^p)$ decoupling estimate using this decomposition, for th
Externí odkaz:
http://arxiv.org/abs/2403.18431
The matrix $p \rightarrow q$ norm is a fundamental quantity appearing in a variety of areas of mathematics. This quantity is known to be efficiently computable in only a few special cases. The best known algorithms for approximately computing this qu
Externí odkaz:
http://arxiv.org/abs/2311.07677
Autor:
Guth, Larry, Maldague, Dominique
We use high-low frequency methods developed in the context of decoupling to prove sharp (up to $C_\epsilon R^\epsilon$) square function estimates for the moment curve $(t,t^2,\ldots,t^n)$ in $\mathbb{R}^n$. Our inductive scheme incorporates sharp squ
Externí odkaz:
http://arxiv.org/abs/2309.13759
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 paper, we generalize the multilinear method of Bourgain and Guth for the
Externí odkaz:
http://arxiv.org/abs/2308.06427
We extend the small cap decoupling program established by Demeter, Guth, and Want to paraboloids in $\mathbb{R}^n$ for some range of $p$.
Comment: 17 pages, small corrections following referee report
Comment: 17 pages, small corrections following referee report
Externí odkaz:
http://arxiv.org/abs/2307.06445
Let $\gamma:[0,1]\rightarrow \mathbb{S}^{2}$ be a non-degenerate curve in $\mathbb{R}^3$, that is to say, $\det\big(\gamma(\theta),\gamma'(\theta),\gamma''(\theta)\big)\neq 0$. For each $\theta\in[0,1]$, let $l_\theta=\{t\gamma(\theta):t\in\mathbb{R}
Externí odkaz:
http://arxiv.org/abs/2209.15152
Autor:
Gan, Shengwen, Guo, Shaoming, Guth, Larry, Harris, Terence L. J., Maldague, Dominique, Wang, Hong
Let $\gamma:[0,1]\rightarrow \mathbb{S}^{2}$ be a non-degenerate curve in $\mathbb{R}^3$, that is to say, $\det\big(\gamma(\theta),\gamma'(\theta),\gamma"(\theta)\big)\neq 0$. For each $\theta\in[0,1]$, let $V_\theta=\gamma(\theta)^\perp$ and let $\p
Externí odkaz:
http://arxiv.org/abs/2207.13844
Publikováno v:
Forum Math. Pi, vol. 12 (2024) art. e2
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 $k$ copies of $\mathbb CP^2$ for $k \ge 4$, then we prove that the maximu
Externí odkaz:
http://arxiv.org/abs/2207.12347