From spaces of polygons to spaces of polyhedra following Bavard, Ghys and Thurston
From spaces of polygons to spaces of polyhedra following Bavard, Ghys and Thurston
After work of W. P. Thurston, C. Bavard and \'E. Ghys constructed particular hyperbolic polyhedra from spaces of deformations of Euclidean polygons. We present this construction as a straightforward consequence of the theory of mixed-volumes. The gluing of these polyhedra can be isometrically embedded into complex hyperbolic cone-manifolds constructed by …