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.