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arXiv · 2110.08441

Decoupling for smooth surfaces in $\mathbb{R}^3$

Jianhui Li·Tongou Yang
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Abstract

For each $d\geq 0$, we prove decoupling inequalities in $\mathbb R^3$ for the graphs of all bivariate polynomials of degree at most $d$ with bounded coefficients, with the decoupling constant depending uniformly in $d$ but not the coefficients of each individual polynomial. As a consequence, we prove a decoupling inequality for (a compact piece of) every smooth surface in $\mathbb{R}^3$, which in particular solves a conjecture of Bourgain, Demeter and Kemp.

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Jianhui Li, Tongou Yang. 2021-10-16. Decoupling for smooth surfaces in $\mathbb{R}^3$. https://arxiv.org/abs/2110.08441

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