Title：On the polar Orlicz-Minkowski problems

Speaker：朱保成  教授  （湖北民族大学）

Time：2018年10月12日（周五）   上午 10:00-11:00

Room：东区管理科研楼  数学科学学院1418室

Abstract：We will talk about the polar Orlicz-Minkowski problems: under what conditions on a nonzero finite measure and a continuous function $/varphi:(0,/infty)/to (0,/infty)$ there exists a convex body $K/in /Re_0$ such that $K$ is an optimizer of the following optimization problems:

$${/inf//sup}_{|L^{^{^/circ}}|=/omega_n}/left/{/int_{S^{n-1}}/varphi(h_L)d/mu:L/in /Re_0/right/}.$$

The solvability of the polar Orlicz-Minkowski problems is discussed under different conditions. In particular, under certain conditions on$/varphi$, the existence of a solution is proved for a nonzero finite measure $/mu$ on unit sphere $S^{n-1}$ which is not concentrated on any hemisphere of $S^{n-1}$.