论文标题
光滑双曲2曲面的傅立叶限制
Fourier restriction for smooth hyperbolic 2-surfaces
论文作者
论文摘要
我们通过多项式分配方法证明了傅立叶限制估计，用于在三二二二二二匹朗的欧几里得空间中任何足够光滑的双曲过度表面的紧凑子集。我们的方法以至关重要的方式利用潜在双曲线几何形状，这导致了强烈的横向性和相应的“特殊”集合的新颖概念。对于这些特殊集的分裂，我们在液位集中对引理的使用至关重要，也许令人惊讶，以使我们以前的文章具有足够平滑的单变量功能。
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.
