Implicit Function Theorem for systems of polynomial equations with vanishing Jacobian and its application to flexible polyhedra and frameworks
Metric Geometry
2007-05-23 v1 Classical Analysis and ODEs
Abstract
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.
Cite
@article{arxiv.math/0006126,
title = {Implicit Function Theorem for systems of polynomial equations with vanishing Jacobian and its application to flexible polyhedra and frameworks},
author = {Victor Alexandrov},
journal= {arXiv preprint arXiv:math/0006126},
year = {2007}
}
Comments
16 pages