l² decoupling theorem for surfaces in ℝ³

2024/03/27 by Larry Guth, Guth, Larry, Dominique Maldague +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Mathematical Approximation and Integration #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.2403.18431

Abstract

We identify a new way to divide the δ-neighborhood of surfaces M⊂ℝ³ into a finitely-overlapping collection of rectangular boxes S. We obtain a sharp (l²,L^p) decoupling estimate using this decomposition, for the sharp range of exponents 2≤ p≤ 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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