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

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

Small corrections following referee report

References in corpus (2)

• Uniform $l^2$-decoupling in ${\mathbb{R}}^2$ for Polynomials
• Strichartz estimates for the Schroedinger equation on non-rectangular two-dimensional tori