2021/10/16 by Jianhui Li, Li, Jianhui, Tongou Yang +1
Mathematics · #42B99 (Primary) #53A05 (Secondary) #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.2110.08441
openalex publication_date 2021/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For each d≥ 0, we prove decoupling inequalities in \mathbb R3 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 ℝ3, which in particular solves a conjecture of Bourgain, Demeter and Kemp.