Hyperideal polyhedra in the 3-dimensional anti-de Sitter space

in Advances in Mathematics (2022), 404(Paper No. 108441, 61 pp),

We study hyperideal polyhedra in the 3-dimensional anti-de Sitter space AdS3, which are defined as the intersection of the projective model of AdS3 with a convex polyhedron in RP3 whose vertices are all ... [more ▼]

We study hyperideal polyhedra in the 3-dimensional anti-de Sitter space AdS3, which are defined as the intersection of the projective model of AdS3 with a convex polyhedron in RP3 whose vertices are all outside of AdS3 and whose edges all meet AdS3. We show that hyperideal polyhedra in AdS3 are uniquely determined by their combinatorics and dihedral angles, as well as by the induced metric on their boundary together with an additional combinatorial data, and describe the possible dihedral angles and the possible induced metrics on the boundary. [less ▲]