论文标题
Grünbaum的拓扑 - Hadwiger-大规模分配问题
Topology of the Grünbaum--Hadwiger--Ramos problem for mass assignments
论文作者
论文摘要
在本文中，以施尼德（Schnider）和阿克塞罗（Axelrod）弗雷德（Axelrod）\＆soberón的最新作品的启发，我们研究了经典的grünbaum--hadwiger-hadwiger--ramos-ramos群众分区问题，以扩展到大规模分配。使用Fadell-Husseini索引理论，我们证明，对于给定的$ j $ ass分配的家族$μ_1，\ dots，μ_j$在Grassmann歧管上$ g _ {\ ell}（\ el el}（\ r^d）（\ r^d）$和一个给定的整数$ k \ geq 1 $，存在线性uspace $ l^$ l. $ k $ affine超平面在$ l $中以$ l $为群众$μ_1^l，\ dots，μ_j^l $分配给子空间$ l $，但前提是$ d \ d \ geq j +（2^{k-1} -1）2^{\ lfloor \ lfloor \ log_2jj \ rfloor} $。
In this paper, motivated by recent work of Schnider and Axelrod-Freed \& Soberón, we study an extension of the classical Grünbaum--Hadwiger--Ramos mass partition problem to mass assignments. Using the Fadell--Husseini index theory we prove that for a given family of $j$ mass assignments $μ_1,\dots,μ_j$ on the Grassmann manifold $G_{\ell}(\R^d)$ and a given integer $k\geq 1$ there exist a linear subspace $L\in G_{\ell}(\R^d)$ and $k$ affine hyperplanes in $L$ that equipart the masses $μ_1^L,\dots,μ_j^L$ assigned to the subspace $L$, provided that $d\geq j + (2^{k-1}-1)2^{\lfloor\log_2j\rfloor}$.
