arXiv subjects

Dóminique Kemp

Publications and source records attributed to Dóminique Kemp.

2 recordsLinked to original sources

arXiv2024

Decoupling for Ruled Hypersurfaces Generated by a Curve

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 $ϕ$.

math.CA↗

arXiv2021

Decoupling via Scale-based Approximations of Limited Efficacy

We consider the decoupling theory of a broad class of $C^5$ surfaces $\mathbb{M} \subset \mathbb{R}^3$ lacking planar points. In particular, our approach also applies to surfaces which are not graphed by mixed homogeneous polynomials. The study of $\mathbb{M}$ furnishes opportunity to recast iterative linear decoupling in a more general form. Here, Taylor-based analysis is combined with efforts to build a library of canonical surfaces (non-cylindrical in general) by which $\mathbb{M}$ may be approximated for decoupling purposes. The work presented may be generalized to the consideration of other surfaces not addressed.

math.CA↗