$C^m$ Semialgebraic Sections Over the Plane

Charles L. Fefferman; Garving K. Luli

$C^m$ Semialgebraic Sections Over the Plane

Classical Analysis and ODEs 2021-02-02 v3 Algebraic Geometry Complex Variables Logic

Authors: Charles L. Fefferman , Garving K. Luli

Abstract

In this paper we settle the two-dimensional case of a conjecture involving unknown semialgebraic functions with specified smoothness. More precisely, we prove the following result: Let $\mathcal{H}$ be a semialgebraic bundle with respect to $C^m_{loc}\left( \mathbb{R}^{2},\mathbb{R}^{D}\right) .$ If $\mathcal{H}$ has a section, then it has a semialgebraic section.

Keywords

vector bundles bundle theory algebraic geometry

Cite

@article{arxiv.2101.06334,
  title  = {$C^m$ Semialgebraic Sections Over the Plane},
  author = {Charles L. Fefferman and Garving K. Luli},
  journal= {arXiv preprint arXiv:2101.06334},
  year   = {2021}
}

Comments

51 pages. comments welcome

$C^m$ Semialgebraic Sections Over the Plane

Abstract

Keywords

Cite

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