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arXiv · 2003.14140

A geometric lemma for complex polynomial curves with applications in Fourier restriction theory

Jaume de Dios Pont
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Abstract

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 $\gamma(z) = (p_1(z), \dots, p_n(z))$, 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.

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Jaume de Dios Pont. 2020-03-31. A geometric lemma for complex polynomial curves with applications in Fourier restriction theory. https://arxiv.org/abs/2003.14140

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