We extend previous work on the two-dimensional developable tangent surface to its higher dimensional analogues $\mathfrak{ M} \subset \mathbb{ R}^{ n+1}$. The approach here similarly applies cylindrical approximate decoupling at its core, albeit in a new format. However, the presence of additional rulings as $n$ increases necessitates a case-by-case analysis, which in itself reveals interesting aspects of the geometry of $\mathfrak{ M}$. The contributions of this paper can be viewed as culminating in the optimal $\ell^2(L^p)$ decoupling over Frenet boxes approximating a suitably defined, arbitrarily thin neighborhood of a curve $\phi$.
Categories: math.CA