A weakening of the curvature condition in $\mathbb{R}^3$ for $\ell^p$ decoupling

Abstract: The celebrated decoupling theorem of Bourgain and Demeter allows for a decomposition in the $L^p$ norm of functions Fourier supported near curved hypersurfaces $M \subset \mathbb{R}^n$. In this project, we find that the condition of non-vanishing principal curvatures may be weakened. When $M \subset \mathbb{R}^3$, we may allow one principal curvature at a time to vanish, and it is assumed additionally that $M$ is foliated by a canonical family of orthogonal curves having nonzero curvature at every point. We find that $\ell^p$ decoupling over nearly flat subsets of $M$ holds within this context.

analysis of PDEsclassical analysis and ODEsfunctional analysis

Audience: researchers in the topic

OARS Online Analysis Research Seminar

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