Abstract: In this talk we will show that a planar graph is the1-skeleton of a Euclidean polyhedron inscribed in a hyperboloid if and only if it is the 1-skeleton of a Euclidean polyhedron inscribed in a cylinder if and only if it is the 1-skeleton of a polyhedron inscribed in a sphere and has a Hamiltonian cycle. That result originates in statements on the geometry of ideal AdS and HP polyhedra. Any hyperbolic metric on the sphere with N labelled cusps, and a distinguished ``equator'' and ``top'' and ``bottom'' polygon, can be uniquely realized as the induced metric on a convex ideal polyhedron in the anti-de Sitter space. Moreover we characterize the possible dihedral angles of the convex ideal AdS (or HP) polyhedra, and show that each ideal polyhedron is characterized by its angles. (This is a joint work with J Danciger and J-M Schlenker.)
Donnerstag, den 10. Juli 2014 um 09.30 Uhr, in INF 288, HS 3 Donnerstag, den 10. Juli 2014 at 09.30, in INF 288, HS 3
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Dr. Anna Wienhard