Yao-Yao分拆定理和中心截线定理的推广
Generalizations of the Yao-Yao partition theorem and the central transversal theorem
摘要：
我们推广了姚-姚划分定理，证明对于$R^d$中的任何光滑测度，都存在使用$(t+1)2^{d-1}$凸区域的等分，使得每个超平面至少错过$t$区域的内部。此外，我们提出了严格的界限上的最小数量的超平面，其工会包含的边界的均分到$n$地区的措施。我们还提出了一个简单的证明Borsuk-Ulam型定理Stiefel流形，使我们能够推广的中心横截定理和证明结果桥接姚-姚分割定理和中心横截定理。
英文摘要：
We generalize the Yao-Yao partition theorem by showing that for any smooth measure in $R^d$ there exist equipartitions using $(t+1)2^{d-1}$ convex regions such that every hyperplane misses the interior of at least $t$ regions. In addition, we present tight bounds on the smallest number of hyperplanes whose union contains the boundary of an equipartition of a measure into $n$ regions. We also present a simple proof of a Borsuk-Ulam type theorem for Stiefel manifolds that allows us to generalize the central transversal theorem and prove results bridging the Yao--Yao partition theorem and the central transversal theorem.
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