Implicit Function Theorem for systems of polynomial equations with vanishing Jacobian and its application to flexible polyhedra and frameworks
| dc.creator | Alexandrov, Victor | |
| dc.date | 2000-06-19 | |
| dc.date.accessioned | 2026-07-07T04:35:56Z | |
| dc.date.available | 2026-07-07T04:35:56Z | |
| dc.description | We study the existence problem for a local implicit function determined by a system of nonlinear algebraic equations in the particular case when the determinant of its Jacobian matrix vanishes at the point under consideration. We present a system of sufficient conditions that implies existence of a local implicit function as well as another system of sufficient conditions that guarantees absence of a local implicit function. The results obtained are applied to proving new and classical results on flexibility and rigidity of polyhedra and frameworks. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/math/0006126 | |
| dc.identifier | http://arxiv.org/abs/math/0006126 | |
| dc.identifier | Monatsh. Math. 132, 269-288 (2001) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59425 | |
| dc.subject | Metric Geometry | |
| dc.subject | Classical Analysis and ODEs | |
| dc.title | Implicit Function Theorem for systems of polynomial equations with vanishing Jacobian and its application to flexible polyhedra and frameworks | |
| dc.type | text |