Fourier restriction for smooth hyperbolic 2-surfaces

2020/10/20 by Buschenhenke, Stefan, Müller, Detlef, Vargas, Ana · 2 citations
#42B10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2010.10449

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.

Cited by

• Restriction estimates for 2D surfaces of finite type 3 and applications to dispersive equations
• Curved Kakeya sets for generic phases in odd dimensions

Related

• Some remarks on Fourier restriction estimates
• A Fourier restriction theorem for a perturbed hyperbolic paraboloid
• Slicing surfaces and Fourier restriction conjecture
• A Fourier restriction theorem for a perturbed hyperbolic paraboloid: polynomial partitioning
• Fourier restriction estimates for surfaces of co-dimension two in ℝ⁵