Equipartitions and Mahler volumes of symmetric convex bodies
Equipartitions and Mahler volumes of symmetric convex bodies
复制标题
对称凸体的均分和马勒体积
DOI：
10.1353/ajm.2022.0027
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发表时间：
2019
影响因子：
1.7
通讯作者：
A. Zvavitch
中科院分区：
文献类型：
--
作者：
M. Fradelizi;Alfredo Hubard;M. Meyer;E. Rold'an;A. Zvavitch
摘要：本文根据Iriyeh和柴田的思想，给出了对称凸体的三维Mahler猜想的一个简短证明。我们的贡献包括，特别是，简单的自我包含证明他们的两个关键声明。第一个是均分（火腿三明治型）定理，完善了著名的结果Hadwiger，并像往常一样，可以证明使用思想从等变拓扑。第二个是产品体积与某些部分及其对偶区域的面积相关的不等式。最后，我们给出了另一种证明的凸体的特征，实现平等的情况下，建立一个新的稳定性结果。
abstract:Following ideas of Iriyeh and Shibata we give a short proof of the three-dimensional Mahler conjecture for symmetric convex bodies. Our contributions include, in particular, simple self-contained proofs of their two key statements. The first of these is an equipartition (ham sandwich type) theorem which refines a celebrated result of Hadwiger and, as usual, can be proved using ideas from equivariant topology. The second is an inequality relating the product volume to areas of certain sections and their duals. Finally we give an alternative proof of the characterization of convex bodies that achieve the equality case and establish a new stability result.
GrünbaumâHadwigerâRamos 超平面质量分配问题的拓扑
影响因子：
1.3
作者：
Blagojević;Pavle V M;Florian;Albert;Ziegler;Günter M
通讯作者：
Günter M