Academic Report of School of Mathematical Sciences [2025] No. 122

(Series Report for High-Level University Construction No. 1224)

Title: Sharp quantitative stability for the Minkowski first inequality via an optimal quadratic estimate for the cone-volume measure

Speaker: Professor Xiong Ge (Tongji University)

Time: 10:00-11:00, November 21, 2025 (Friday)

Location: Room 2433, Huiwen Building, Yuehai Campus, Shenzhen University

Abstract:

An optimal quadratic estimate for the cone-volume measure of a pair of antipodal points in Rn is obtained. As applications of this estimate, a strong Minkowski first inequality and therefore a strong Brunn-Minkowski inequality, and a strong reverse isoperimetric inequality for the Lutwak-Yang-Zhang functional, are established.

Speaker Biography:

Xiong Ge is a Tenured Professor and Doctoral Supervisor at Tongji University. His research primarily focuses on convex geometry. Professor Xiong has resolved several open problems in convex geometry, including the 2- and 3-dimensional cases of the Lutwak-Yang-Zhang extremal problem for the cone-volume functional, the 2-dimensional case of the Baker-Larman problem concerning the determination of convex bodies by their sections, and he and his students were the first to propose and solve the Minkowski problem for Lp capacitary measures. He also completely resolved the problem posed by Professor G. Zhang of New York University regarding the consistency of the John ellipsoid and the dual inertia ellipsoid for convex bodies. Professor Xiong has published over 30 papers in important international pure mathematics journals, including Journal of Differential Geometry, Advances in Mathematics, Indiana University Mathematics Journal, International Mathematics Research Notices, Calculus of Variations and Partial Differential Equations, Bulletin of the London Mathematical Society, Journal of Functional Analysis, Communications in Analysis and Geometry, and Discrete & Computational Geometry. Some of his results have been incorporated into classic textbooks on convex geometry, such as Geometric Tomography and Convex Bodies: The Brunn-Minkowski Theory.

All faculty and students are welcome!

Host: Wang Yingnan

School of Mathematical Sciences

November 18, 2025