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arXiv · 2101.06334

$C^m$ Semialgebraic Sections Over the Plane

Charles L. Fefferman·Garving K. Luli
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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.

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BibTeXRIS

Charles L. Fefferman, Garving K. Luli. 2021-01-16. $C^m$ Semialgebraic Sections Over the Plane. https://arxiv.org/abs/2101.06334

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