报告题目 (Title)：On the sine polarity and the L_p-sine Blaschke-Santaló inequality（正弦极体和 L_p-正弦Blaschke-Santaló不等式）

报告人 (Speaker)：李爱军（浙江科技大学）

报告时间 (Time)：2024年4月18日(周四) 11:10

报告地点 (Place)：校本部GJ303

邀请人(Inviter)：席东盟、李晋、张德凯、吴加勇

主办部门：理学院数学系

报告摘要：This talk is dedicated to study the sine version of polar bodies and establish the L_p-sine Blaschke-Santaló inequality for the L_p-sine centroid body. The L_p-sine centroid body〖 Λ〗_p K for a star body K is a convex body based on the L_p-sine transform, and its associated Blaschke-Santaló inequality provides an upper bound for the volume of Λ_p^° K, the polar body of Λ_p K, in terms of the volume of K. Thus, this inequality can be viewed as the “sine cousin” of the〖 L〗_p Blaschke-Santaló inequality established by Lutwak and Zhang. As p→∞, the limit of Λ_p^° K becomes the sine polar body K^⋄ and hence the L_p-sine Blaschke-Santaló inequality reduces to the sine Blaschke-Santaló inequality for the sine polar body. The sine polarity naturally leads to a new class of convex bodies C_e^n, which consists of all origin-symmetric convex bodies generated by the intersection of origin-symmetric closed solid cylinders. Many notions inC_e^nare developed, including the cylindrical support function, the supporting cylinder, the cylindrical Gauss image, and the cylindrical hull. Based on these newly introduced notions, the equality conditions of the sine Blaschke-Santaló inequality are settled.