Rigidity of bordered polyhedral surfaces (Q2677326)

A Euclidean (or spherical or hyperbolic) polyhedral surface is meant to be a triangulated surface \((S,T)\) equipped with a metric \(d\) such that every triangle is isometric to a Euclidean (or spherical or hyperbolic) triangle. In the situation that \(S\) has a non-empty boundary, the main result gives characterizations of \(d\) up to isometry by its boundary values and several curvature quantities on the interior edges of \(T\). Corollaries concern results on cyclic polygons and on metrics associated to circle packings.