The volume product of convex bodies with many hyperplane symmetries
The volume product of convex bodies with many hyperplane symmetries
复制标题
具有多个超平面对称性的凸体的体积积
DOI：
10.1353/ajm.2013.0018
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发表时间：
2013
影响因子：
1.7
通讯作者：
M. Fradelizi
中科院分区：
文献类型：
--
作者：
F. Barthe;M. Fradelizi
马勒猜想预言了凸体极点体积的一个锐利下界。我们在以下意义上证实了具有许多超平面对称性的凸体的猜想：它们的对称性的超平面有一点相交。此外，我们还得到了某些反射群不变的凸体的改进的锐化下界，即正多面体的等距群的直积。
Mahler’s conjecture predicts a sharp lower bound on the volume of the polar of a convex body in terms of its volume. We confirm the conjecture for convex bodies with many hyperplane symmetries in the following sense: their hyperplanes of symmetries have a one-point intersection. Moreover, we obtain improved sharp lower bounds for classes of convex bodies which are invariant by certain reflection groups, namely direct products of the isometry groups of regular polytopes.