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题目: On the polar Orlicz-Minkowski problems and the p-capacitary Orlicz-Petty bodies 




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

$$\inf/sup_{|L|=\omega_n}\{\int_{S^{n-1}}\varphi(h_L)d\mu;L\in \mathcal{R}_0\}.$$

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 $S^{n-1}$. Another part of this paper deals with the p-capacitary Orlicz-Petty bodies. In particular, the existence of the p-capacitary Orlicz-Petty bodies is established and the continuity of the p-capacitary Orlicz-Petty bodies is proved.


时间: 2018年4月11日 14:00--16:00




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