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Salem not are Cones
作者:      发布时间:2023-11-29       点击数:
报告时间 2023-12-06 9时-11时 报告地点 腾讯会议:626734082
报告人 JUNJIE ZHU

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9-11点

报告地点:线上, 腾讯会议:626734082

 

专家简介:

JUNJIE ZHUBC. 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.

 


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