Scale-invariant Fourier restriction to a hyperbolic surface

Stovall, Betsy

doi:10.2140/apde.2019.12.1215

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Scale-invariant Fourier restriction to a hyperbolic surface

Betsy Stovall

Vol. 12 (2019), No. 5, 1215–1224

DOI: 10.2140/apde.2019.12.1215

Abstract

This result sharpens the bilinear-to-linear deduction of Lee and Vargas for extension estimates on the hyperbolic paraboloid in $ℝ^{3}$ to the sharp line, leading to the first scale-invariant restriction estimates, beyond the Stein–Tomas range, for a hypersurface on which the principal curvatures have different signs.

Keywords

Fourier restriction, bilinear restriction, hyperbolic restriction

Mathematical Subject Classification 2010

Primary: 42B20

Milestones

Received: 8 September 2017

Revised: 6 August 2018

Accepted: 17 September 2018

Published: 15 December 2018

Authors

Betsy Stovall
Department of Mathematics University of Wisconsin Madison, WI United States

Vol. 12, No. 5, 2019