A restriction estimate using polynomial partitioning

Guth, Larry

doi:10.1090/jams827

A restriction estimate using polynomial partitioning
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by Larry Guth

J. Amer. Math. Soc. 29 (2016), 371-413

DOI: https://doi.org/10.1090/jams827

Published electronically: May 11, 2015

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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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