Rigidity of bordered polyhedral surfaces. (English) Zbl 1510.52014
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.
Reviewer: Christian Richter (Jena)
MSC:
| 52C25 | Rigidity and flexibility of structures (aspects of discrete geometry) |
| 51M04 | Elementary problems in Euclidean geometries |
| 51M09 | Elementary problems in hyperbolic and elliptic geometries |
| 52C26 | Circle packings and discrete conformal geometry |
Keywords:
bordered polyhedral surface; metric; rigidity; boundary value; discrete curvature; cyclic polygon; circle packing metricSoftware:
CirclePackReferences:
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