On locally convex PL-manifolds and fast verification of convexity
| dc.creator | Rybnikov, Konstantin | |
| dc.date | 2003-09-23 | |
| dc.date | 2003-11-24 | |
| dc.date.accessioned | 2026-07-07T05:01:22Z | |
| dc.date.available | 2026-07-07T05:01:22Z | |
| dc.description | We show that a realization of a closed connected PL-manifold of dimension n-1 in Euclidean n-space (n>2) is the boundary of a convex polyhedron if and only if the interior of each (n-3)-face has a point, which has a neighborhood lying on the boundary of a convex n-dimensional body. This result is derived from a generalization of Van Heijenoort's theorem on locally convex manifolds to spherical spaces. We also give a brief analysis of how local convexity and topology of non-compact surfaces are related to global convexity in the hyperbolic space. Our convexity criterion for PL-manifolds imply an easy polynomial-time algorithm for checking convexity of a given closed compact PL-surface in Euclidean of spherical space of dimension n>2. | |
| dc.description | 10 pages (abbreviated version). Significantly different from all older versions. Discount the previous version -- it had many omissions and typos, like the following one: indeed, everything works starting from dimension n=3, not n=2 as was printed in the old abstract. Hyperbolic and spherical cases have been substantially rewritten and errors fixed. This preprint is close to a similar preprint on the CS part of arxiv.org | |
| dc.identifier | https://arxiv.org/abs/math/0309370 | |
| dc.identifier | http://arxiv.org/abs/math/0309370 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68642 | |
| dc.subject | Metric Geometry | |
| dc.subject | Primary: 52B70; Secondary: 52A58, 68Q25, 68U05 | |
| dc.title | On locally convex PL-manifolds and fast verification of convexity | |
| dc.type | text |