Duality of floating and illumination bodies
Duality of floating and illumination bodies
复制标题
漂浮体和照明体的二元性
DOI：
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复制
发表时间：
2017
影响因子：
1.1
通讯作者：
E. Werner
中科院分区：
文献类型：
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作者：
Olaf Mordhorst;E. Werner
我们调查的浮动和照明机构之间的对偶关系。这两个物体的定义表明，漂浮物体的极性应该类似于极性的照明体。我们考虑中心对称凸体类的这个问题。我们提供了精确的估计$（B_p^n）$和中心对称凸体的处处正高斯曲率。我们的估计表明，平等的极性的浮动机构和照明机构的极性只能在椭球的情况下才能实现。
We investigate a duality relation between floating and illumination bodies. The definitions of these two bodies suggest that the polar of the floating body should be similar to the illumination body of the polar. We consider this question for the class of centrally symmetric convex bodies. We provide precise estimates for $(B_p^n)$ and for centrally symmetric convex bodies with everywhere positive Gauss curvature. Our estimates show that equality of the polar of the floating body and the illumination body of the polar can only be achieved in the case of ellipsoids.