Fourier restriction for smooth hyperbolic 2-surfaces

We prove Fourier restriction estimates by means of the polynomial partitioning method for compact subsets of any sufficiently smooth hyperbolic hypersurface in 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.

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