Bang’s problem and symplectic invariants
Bang’s problem and symplectic invariants
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Bang 问题和辛不变量
DOI：
10.4310/jsg.2019.v17.n6.a1
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发表时间：
2014
影响因子：
0.7
通讯作者：
F. Petrov
中科院分区：
文献类型：
--
作者：
A. Akopyan;R. Karasev;F. Petrov
我们考虑了凸体被木板覆盖的Tarski-Bang问题。这类结果给出了覆盖给定凸体的板(一对平行超平面之间的区域)的宽度和的下界。
以前我们已经应用了辛几何的一些概念来研究凸体，在这里我们展示了辛技术在这个问题上也是有用的。我们能够用辛技巧处理一些特殊情况，并表明一般情况是由K~Ball的结果推动的辛几何中的某种“次可加性猜想”。我们还用更初等的方法证明了几个相关结果。
We consider the Tarski--Bang problem about covering of convex bodies by planks. The results of this kind give a lower bound on the sum of widths of planks (regions between a pair of parallel hyperplanes) covering a given convex body.
Previously we have applied some notions of symplectic geometry to study convex bodies, and here we show that the symplectic techniques may be useful in this problem as well. We are able to handle some particular cases with the symplectic techniques, and show that the general cases would follow from a certain ``subadditivity conjecture'' in symplectic geometry, motivated by the results of K.~Ball. We also prove several related results by more elementary methods.