Orlicz曲率像

Orlicz Curvature Images

【目的】把L_p中的p-曲率像推广为Orlicz曲率像。【方法】应用凸几何分析。【结果】对Orlicz曲率函数进行定义,并推广了Orlicz混合体积。【结论】得到Orlicz曲率像的仿射不变性等一些重要性质及关于Orlicz曲率像的几个不等式,特殊情形为Lutwak得到的Lp中的相应结果。

[Purposes]To investigate the curvature image is to generalize the p-curvature image in L_p to Orlicz curvature image.[Methods]Convex geometric analysis,it introduces the concept of Orlicz curvature functions and generalize the Orlicz mixed volume.[Findings]Obtain some important properties including affine invariant and inequalities of Orlicz curvature image.[Conclusions]As their special cases,some Lutwak＇s results in Lpis obtained.