报告名称：Salem not are Cones

报告专家：JUNJIE ZHU

专家所在单位：英属哥伦比亚大学

报告时间：2023-12-06 上午9点-11点

报告地点:线上, 腾讯会议：626734082

专家简介：

JUNJIE ZHU，BC. Vancouver, (UBC), Columbia British of UBC,University at Instructor Class Mathematics,Small in Candidate Ph.D.

报告摘要：

The notions of Hausdorff and Fourier dimensions are ubiquitous in harmonic analysis and geometric measure theory. It is known that any hypersurface in Rd+1 has Hausdorff dimension d. However, the Fourier dimension depends on the finer geometric properties of the hypersurface. For instance, the Fourier dimension of a hyperplane is 0, and the Fourier dimension of a hypersurface with non-vanishing Gaussian curvature is d. Recently, Harris has shown that the Euclidean light cone in Rd+1 has Fourier dimension d − 1, which leads one to conjecture that the Fourier dimension of a hypersurface equals the number of non-vanishing principal curvatures. We prove this conjecture for all d-dimensional cones in Rd+1 generated by hypersurfaces in Rd with non-vanishing Gaussian curvature. In particular, cones are not Salem. Our method involves substantial generalizations of Harris’s strategy.