论文标题
用于复杂多项式曲线的几何引理，并在傅立叶限制理论中应用
A geometric lemma for complex polynomial curves with applications in Fourier restriction theory
论文作者
论文摘要
本文的目的是证明在$ \ Mathbb r^{2n} $中的某些$ 2- $尺寸表面的统一傅立叶限制估计。这些表面是复杂多项式曲线的图像$γ（z）=（p_1（z），\ dots，p_n（z））$，配备了相当于仿射弧度度量的复合物。该结果是在实际环境中由Stovall [Sto16]与先前结果相比的复杂多项式对应物。作为证明该定理的一种手段，我们提供了Dendrinos和Wright [DW10]的几何不等式的替代证明，该证明将结果扩展到复杂的多项式。
The aim of this paper is to prove a uniform Fourier restriction estimate for certain $2-$dimensional surfaces in $\mathbb R^{2n}$. These surfaces are the image of complex polynomial curves $γ(z) = (p_1(z), \dots, p_n(z))$, equipped with the complex equivalent to the affine arclength measure. This result is a complex-polynomial counterpart to a previous result by Stovall [Sto16] in the real setting. As a means to prove this theorem we provide an alternative proof of a geometric inequality by Dendrinos and Wright [DW10] that extends the result to complex polynomials.
