【摘要】 本文运用Aleksandrov-Fenchel不等式,首先推广了Lutwak,Bonnesen和Fenchel等建立的三个有用的定理,这三个定理在解决某些唯一性问题中扮演着重要角色.然后,把这些结果从一般的混合体积和投影体推广到混合投影体的极和混合仿射表面积上,获得了一些较理想的结果.更多还原

【Abstract】 By using the Aleksandrov-Fenchel inequalities, the authors first generalize Lutwak and Bonnesen-Fenchel’s three important theorems which have been very valuable in answering a variety of uniqueness questions. Then, the authors improve above results from mixed volume and projection bodies to the polars of mixed projection bodies and affine surface area, and get some analogous results.更多还原