Fourier restriction for smooth hyperbolic 2-surfaces
Classical Analysis and ODEs
2020-10-21 v1
Abstract
We prove Fourier restriction estimates by means of the polynomial partitioning method for compact subsets of any sufficiently smooth hyperbolic hypersurface in threedimensional euclidean space. Our approach exploits in a crucial way the underlying hyperbolic geometry, which leads to a novel notion of strong transversality and corresponding "exceptional" sets. For the division of these exceptional sets we make crucial and perhaps surprising use of a lemma on level sets for sufficiently smooth one-variate functions from a previous article of ours.
Cite
@article{arxiv.2010.10449,
title = {Fourier restriction for smooth hyperbolic 2-surfaces},
author = {Stefan Buschenhenke and Detlef Müller and Ana Vargas},
journal= {arXiv preprint arXiv:2010.10449},
year = {2020}
}