2021/04/08 by Dóminique Kemp, Kemp, Dóminique · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2104.04115
openalex publication_date 2021/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the decoupling theory of a broad class of C5 surfaces \mathbbM ⊂ ℝ3 lacking planar points. In particular, our approach also applies to surfaces which are not graphed by mixed homogeneous polynomials. The study of \mathbbM 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 \mathbbM may be approximated for decoupling purposes. The work presented may be generalized to the consideration of other surfaces not addressed.