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

Jaume de Dios Pont
2020 arXiv   pre-print
The aim of this paper is to prove a uniform Fourier restriction estimate for certain 2-dimensional surfaces in R^2n. These surfaces are the image of complex polynomial curves γ(z) = (p_1(z), ..., 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
more » ... DW10] that extends the result to complex polynomials.
arXiv:2003.14140v1 fatcat:wazwgt7ptnafbcxr7532e4jyva