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$\ell^2$ decoupling
theorem for surfaces in $\mathbb{R}^3$
Larry Guth, Dominique Maldague and Changkeun Oh |
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Vol. 19 (2026), No. 1, 167–202
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Abstract |
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We identify a new way to divide the -neighborhood of surfaces into a finitely overlapping collection of rectangular boxes . We obtain a sharp decoupling estimate using this decomposition for the sharp range of exponents . Our decoupling inequality leads to new exponential sum estimates where the frequencies lie on surfaces which do not contain a line. |
Keywords
decoupling inequality, exponential sum
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Mathematical Subject Classification
Primary: 42B25
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Milestones
Received: 27 March 2024
Revised: 6 October 2024
Accepted: 8 January 2025
Published: 26 November 2025
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Authors |
| Larry Guth | |
| Department of Mathematics Massachusetts Institute of Technology Cambridge, MA United States |
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| Dominique Maldague | |
| Department of Mathematics Massachusetts Institute of Technology Cambridge, MA United States |
Department of Mathematics University of Cambridge Cambridge United Kingdom |
| Changkeun Oh | |
| Department of Mathematics Massachusetts Institute of Technology Cambridge, MA United States |
Department of Mathematical Sciences
and RIM Seoul National University Seoul South Korea |
| © 2026 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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