Polygonal surfaces in pseudo-hyperbolic spaces

A polygonal surface in the pseudo-hyperbolic space \(H^{(2,n)}\) is a complete maximal surface bounded by a lightlike polygon with finitely many vertices. We give several characterizations of these surfaces. Polygonal surfaces are characterized by finiteness of their total curvature and by asymptotic flatness.

The goal of the talk is to explain some constructions coming from nonpositive curvature geometry to establish the equivalence between being polygonal and having finite total curvature.