报告题目：On the sine polarity and theLp-sine Blaschke-Santaló inequality

报告人：李爱军 教授 浙江科技学院

邀请人：马如云教授

报告时间：2023年6月11日（周日）20:00-21:00

腾讯会议：573-724-395

报告摘要：This talk is dedicated to study the sine version of polar bodies and establish the Lp-sine Blaschke-Santaló inequality

for the Lp-sine centroid body. The Lp-sine centroid body$\Lambda_p K$ for a star body K is a convex body basedon the Lp-sine transform, and its associatedBlaschke-Santaló inequality provides an upper bound for thevolume of $\Lambda_p^{\circ}K$, the polar body of $\Lambda_p K$, interms of the volume of K. Thus, this inequality can be viewed asthe “sine cousin” of the Lp Blaschke-Santalóinequalityestablished by Lutwak and Zhang. As $p\rightarrow \infty$, the limit of $\Lambda_p^{\circ} K$ becomesthe sine polar body $K^{\diamond}$ and hence the Lp-sineBlaschke-Santaló inequality reduces to the sineBlaschke-Santaló inequality for the sine polar body. The sinepolarity naturally leads to a new class of convex bodies $\mathcal{C}_{e}^n$, which consists of all origin-symmetric convexbodies generated by the intersection of origin-symmetric closedsolid cylinders. Many notions in $\mathcal{C}_{e}^n$ are developed,including the cylindrical support function, the supporting cylinder,the cylindrical Gauss image, and the cylindrical hull. Based onthese newly introduced notions, the equality conditions of the sineBlaschke-Santaló inequality are settled.

报告人简介：李爱军，博士，美国纽约大学理工学院博士后，现浙江科技学院教授，硕士研究生导师，美国数学评论评论员，主要从事凸几何分析和几何不等式的研究，分别在2015和2022年应邀参加了加拿大数学年会并做报告，2019年应邀参加在清华大学举办的第八届华人数学家大会(ICCM)，并做45分钟邀请报告。参与国家自然科学基金重点项目一项，主持完成国家自然科学基金项目一项，参与完成一项。先后在J. Funct. Anal.，Adv. Math., J. London Math. Soc., J. Geom. Anal., IMRN, Math. Z.等杂志上发表SCI论文三十余篇。