论文标题
多边形的模量和多面体的变形
Moduli spaces of polygons and deformations of polyhedra with boundary
论文作者
论文摘要
我们证明了Ian Agol的猜想：多面体表面的所有等距实现，边界在多形构成边界的多边形的Kapovich-Millson Moduli空间中扫除了各向同性子集。对于通用的多面体磁盘，我们显示其等距实现的边界构成了拉格朗日子集。作为此结果的应用，我们为Richard Kenyon的问题获得了一个新的解决方案，内容涉及跨越R^3中的单位间隔组成的分段线性曲线。
We prove a conjecture of Ian Agol: all isometric realizations of a polyhedral surface with boundary sweep out an isotropic subset in the Kapovich-Millson moduli space of polygons isomorphic to the boundary. For a generic polyhedral disk we show that boundaries of its isometric realizations make up a Lagrangian subset. As an application of this result, we obtain a new solution to the problem of Richard Kenyon about spanning domes of piecewise linear curves comprised of unit intervals in R^3.
