This research demonstrates decoupling inequalities for bivariate polynomials and smooth surfaces, highlighting a significant mathematical conjecture.
For each d≥ 0, we prove decoupling inequalities in R³ for the graphs of all bivariate polynomials of degree at most d with bounded coefficients, with the decoupling constant uniform in the coefficients of those polynomials. 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.
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Li et al. (2025) studied this question.
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