Elasticae and inradius

Antoine Henrot; Othmane Mounjid

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arXiv · 1608.00727

Elasticae and inradius

Antoine Henrot·Othmane Mounjid

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Abstract

The elastic energy of a planar convex body is defined by $E(\Om)=\frac 12\,\int\_{\partial\Om} k^2(s)\,ds$where $k(s)$ is the curvature of the boundary. In this paper we are interested in the minimization problemof $E(\Om)$ with a constraint on the inradius of $\Om$. By contrast with all the other minimization problemsinvolving this elastic energy (with a perimeter, area, diameter or circumradius constraints) for which thesolution is always the disk, we prove here that the solution of this minimization problem is not the disk and we completely characterizeit in terms of elementary functions.

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Antoine Henrot, Othmane Mounjid. 2016-08-02. Elasticae and inradius. https://arxiv.org/abs/1608.00727

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