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arXiv · 2407.05225

Decoupling for Ruled Hypersurfaces Generated by a Curve

Dóminique Kemp
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Abstract

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 $\phi$.

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Dóminique Kemp. 2024-07-07. Decoupling for Ruled Hypersurfaces Generated by a Curve. https://arxiv.org/abs/2407.05225

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