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

作者：Chen, Qiyu; Schlenker, Jean-Marc^*

来源：Advances in Mathematics, 2022, 404: 108441.

DOI：10.1016/j.aim.2022.108441

• Hyperideal polyhedra
• Anti-de Sitter
• Dihedral angle
• Induced metric

We study hyperideal polyhedra in the 3-dimensional anti-de Sitter space AdS(3), which are defined as the intersection of the projective model of AdS(3) with a convex polyhedron in RP3 whose vertices are all outside of AdS(3) and whose edges all meet AdS(3). We show that hyperideal polyhedra in AdS(3) 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.

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