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# Title:A restriction estimate using polynomial partitioning

Authors:Larry Guth
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.
 Comments: 42 pages. Minor revisions. Accepted for publication in JAMS Subjects: Classical Analysis and ODEs (math.CA) Cite as: arXiv:1407.1916 [math.CA] (or arXiv:1407.1916v3 [math.CA] for this version)

## Submission history

From: Larry Guth [view email]
[v1] Tue, 8 Jul 2014 00:42:27 UTC (39 KB)
[v2] Mon, 4 Aug 2014 21:19:22 UTC (39 KB)
[v3] Mon, 2 Feb 2015 22:43:53 UTC (40 KB)
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