报告名称：construction of curved Kakeya sets

报告专家：杨童鸥

专家所在单位：南方科技大学

报告时间：2025-10-27 14:30-15:30

报告地点:腾讯线上

专家简介： 杨童鸥博士现为南方科技大学数学系助理教授，博士毕业于加拿大英属哥伦比亚大学，其后在美国从事博士后研究工作数年。其领域为调和分析及几何测度论，在American Journal of Mathematics及Mathematische Annalen等国际期刊发表论文数篇。

报告摘要：A spherical Kakeya set is a subset of R^n of zero Lebesgue measure that contains a sphere of every radius. Kolasa-Wolff (1999) proved the existence of spherical Kakeya sets by applying a BRK-type construction. We generalise their construction to C^{2,alpha} hypersurfaces of nonzero Gaussian curvature. Moreover, we are able to improve the measure bound of such curved Kakeya sets; in particular, this bound is optimal in n=3 up to constant multiples. This is joint with Xianghong Chen and Yue Zhong.