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arXiv · 2403.18431

$l^2$ decoupling theorem for surfaces in $\mathbb{R}^3$

Larry Guth·Dominique Maldague·Changkeun Oh
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Abstract

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 the sharp range of exponents $2\leq p\leq 4$. Our decoupling inequality leads to new exponential sum estimates where the frequencies lie on surfaces which do not contain a line.

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Larry Guth, Dominique Maldague, Changkeun Oh. 2024-03-27. $l^2$ decoupling theorem for surfaces in $\mathbb{R}^3$. https://doi.org/10.2140/apde.2026.19.167

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