Decouplings for Surfaces of Zero Curvature

Abstract

We extend the $l^2(L^p)$ decoupling theorem of Bourgain-Demeter to the full class of developable surfaces in ${\mathbb{R}}^3$. This completes the $l^2$ decoupling theory of the zero Gaussian curvature surfaces that lack planar (or umbilic) points. Of central interest to our study is the tangent surface associated to the moment curve.

2 figures. A few minor corrections and simplifications have been made since the previous submission