A rigidity criterion for non-convex polyhedra
| dc.creator | Schlenker, Jean-Marc | |
| dc.date | 2003-01-28 | |
| dc.date | 2003-01-30 | |
| dc.date.accessioned | 2026-07-07T04:54:44Z | |
| dc.date.available | 2026-07-07T04:54:44Z | |
| dc.description | Let $P$ be a (non necessarily convex) embedded polyhedron in $\R^3$, with its vertices on an ellipsoid. Suppose that the interior of $P$ can be decomposed into convex polytopes without adding any vertex. Then $P$ is infinitesimally rigid. More generally, let $P$ be a polyhedron bounding a domain which is the union of polytopes $C_1, ..., C_n$ with disjoint interiors, whose vertices are the vertices of $P$. Suppose that there exists an ellipsoid which contains no vertex of $P$ but intersects all the edges of the $C_i$. Then $P$ is infinitesimally rigid. The proof is based on some geometric properties of hyperideal hyperbolic polyhedra. | |
| dc.description | 11 pages, 1 image. Revised versions will be posted on http://picard.ups-tlse.fr/~schlenker v2: one statement corrected, ref. added | |
| dc.identifier | https://arxiv.org/abs/math/0301333 | |
| dc.identifier | http://arxiv.org/abs/math/0301333 | |
| dc.identifier | Discrete and Computational Geometry, 33 (2005):2, 207-221. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66376 | |
| dc.subject | Differential Geometry | |
| dc.subject | Metric Geometry | |
| dc.title | A rigidity criterion for non-convex polyhedra | |
| dc.type | text |