On the applications and generalizations of the cone-volume functional
The cone-volume functional was originally introduced by E. Lutwak, D. Yang and G. Zhang (LYZ) in 2001 to attack the celebrated longstanding Schneider projection problem in convex geometry. It is closely related to the cone-volume measure of convex bodies and has strong applications to the reverse affine isoperimetric problem and the logarithmic Minkowski problem.
In this talk, we will first review the fundamental properties of the cone-volume functional and its applications to the Schneider projection problem. Then, we will talk on the solved LYZ conjecture for the cone-volume functional (including our work on this conjecture) and its applications to the logarithmic Minkowski problem. Then we will report our very recent results on its generalizations and applications, including the variational formula and the extreme problem on the mixed cone-volume functional.
This talk is based on the joint work with Hu Jiaqi, Lu Xinbao and Sun Qiang.
Brief Introduction to the Presenter:
Zhao lilu， Professor of the School of Mathematics, Shandong University
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Sponsored by: School of Mathematics, Shandong Unive