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Implicit Function Theorem for systems of polynomial equations with vanishing Jacobian and its application to flexible polyhedra and frameworks | | Victor Alexandrov
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19 Jun 2000 | | Journal: | Monatsh. Math. 132, 269-288 (2001) | | Subject: | Metric Geometry; Classical Analysis and ODEs | math.MG math.CA | | Affiliation: | Sobolev Institute of Mathematics | | 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. | | Source: | arXiv, math.MG/0006126 | | Services: | Forum | Review | PDF | Favorites | |
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