论文标题
双曲线多面体的最大体积
The maximum volume of hyperbolic polyhedra
论文作者
论文摘要
我们使用一些固定组合物和任何形式的顶点（真实，理想或高层）研究双曲线多面体的量的至上。我们发现，至上始终等于1骨骨骼的整流体积。 通过将一种体积增加的流动应用于任何双曲线多面体，可以证明该定理。由于多面体的某些层可能会退化为较低维度的物体，因此流动可能会出现奇异性。发生这种情况时，我们需要仔细研究所得多面体的组合物并继续流动，直到最终得到整流的多面体。
We study the supremum of the volume of hyperbolic polyhedra with some fixed combinatorics and with vertices of any kind (real, ideal or hyperideal). We find that the supremum is always equal to the volume of the rectification of the 1-skeleton. The theorem is proved by applying a sort of volume-increasing flow to any hyperbolic polyhedron. Singularities may arise in the flow because some strata of the polyhedron may degenerate to lower-dimensional objects; when this occurs, we need to study carefully the combinatorics of the resulting polyhedron and continue with the flow, until eventually we get a rectified polyhedron.
