标题： 尖锐双曲$n$-流形的多面体分解与全测地边界 显示英文标题

标题： The polyhedral decomposition of cusped hyperbolic $n$-manifolds with totally geodesic boundary

摘要： 设$M$是一个具有全测地边界的小体积非紧致完备双曲$n$-流形。 我们证明存在$M$的多面体分解，使得每个单元要么是一个理想多面体，要么是一个仅有一个截断面的部分截断多面体。 这个结果与 Epstein-Penner 的理想分解\cite{EP}对于有尖点的双曲流形，以及 Kojima 的截断多面体分解\cite{Kojima}对于具有全测地边界的紧致双曲流形 相对应。 我们采用两种不同的方法来展示本文的主要结果。 我们还证明$M$的多面体分解的数量是有限的。 显示英文摘要

摘要： Let $M$ be a volume finite non-compact complete hyperbolic $n$-manifold with totally geodesic boundary. We show that there exists a polyhedral decomposition of $M$ such that each cell is either an ideal polyhedron or a partially truncated polyhedron with exactly one truncated face. This result parallels Epstein-Penner's ideal decomposition \cite{EP} for cusped hyperbolic manifolds and Kojima's truncated polyhedron decomposition \cite{Kojima} for compact hyperbolic manifolds with totally geodesic boundary. We take two different approaches to demonstrate the main result in this paper. We also show that the number of polyhedral decompositions of $M$ is finite.