A restriction estimate using polynomial partitioning

Larry Guth

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arXiv · 1407.1916

A restriction estimate using polynomial partitioning

Larry Guth

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Abstract

If $S$ is a smooth compact surface in $\mathbb{R}^3$ with strictly positive second fundamental form, and $E_S$ is the corresponding extension operator, then we prove that for all $p > 3.25$, $\| E_S f\|_{L^p(\mathbb{R}^3)} \le C(p,S) \| f \|_{L^\infty(S)}$. The proof uses polynomial partitioning arguments from incidence geometry.

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BibTeX RIS

Larry Guth. 2015-02-02. A restriction estimate using polynomial partitioning. https://arxiv.org/abs/1407.1916

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