Acta Mathematica

Volume 221 (2018)

Number 1

Restriction estimates using polynomial partitioning II

Pages: 81 – 142

DOI: http://dx.doi.org/10.4310/ACTA.2018.v221.n1.a3

Author

Larry Guth (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Ma., U.S.A.)

Abstract

We improve the estimates in the restriction problem in dimension $n \geqslant 4$. To do so, we establish a weak version of a $k$-linear restriction estimate for any $k$. The exponents in this weak $k$-linear estimate are sharp for all $k$ and $n$.

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Received 6 November 2017

Received revised 11 April 2018

Published 6 November 2018