Implicit Function Theorem for systems of polynomial equations with vanishing Jacobian and its application to flexible polyhedra and frameworks

2000/06/19 by Victor Alexandrov · 1 citation
Mathematics · #math.MG #math.CA

paper · pdf

published as Monatsh. Math. 132, 269-288 (2001) · 16 pages

arxiv created 2000/06/19 · arxiv updated 2009/11/30

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.

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• Higher Order Rigidity and Energy

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