On Isometric Embeddings into Anti-de Sitter Spacetimes

Weyl’s theorem was proved independently by Nirenberg [15] and Pogorelov [16] using different approaches. Nirenberg used the continuity method that is more familiar to geometric analysts. The Pogorelov approach consists of two steps. First, Pogorelov exhibited a generalized solution as the limit of polyhedra and then Pogorelov proved the regularity of this generalized solution. Later, Pogorelov generalized the Weyl theorem to hyperbolic space H−κ with sectional curvature −κ: