可分凸区域上的余维$1$单形
Codimension-$1$ Simplices in Divisible Convex Domains
摘要：
在凸可分区域$Ω\subset \mathbb{R} \textrm{P}^d$中适当嵌入的单形的行为有点像黎曼流形中的平面，所以我们称它们为平面。证明了余维$1$平坦集在紧致商流形上有一个不相交的虚$(d-1)$环面的有限集合的象。如果这个虚环面的集合是非空的，那么它的补的分支是具有$d$型尖点的尖点凸射影流形。
英文摘要：
Properly embedded simplices in a convex divisible domain $Ω\subset \mathbb{R} \textrm{P}^d$ behave somewhat like flats in Riemannian manifolds, so we call them flats. We show that the set of codimension-$1$ flats has image which is a finite collection of disjoint virtual $(d-1)$-tori in the compact quotient manifold. If this collection of virtual tori is non-empty, then the components of its complement are cusped convex projective manifolds with type $d$ cusps.
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