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arXiv · 1706.06387

A Weierstrass representation for 2D elasticity

Ulrich Pinkall·Jonas Tervooren
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Abstract

We study a class of elastic energy functionals for maps between planar domains (among them the so-called squared distance functional) whose critical points (elastic maps) allow a far more complete theory than one would expect from general elasticity theory. For some of these functionals elastic maps even admit a "Weierstrass representation" in terms of holomorphic functions, reminiscent of the one for minimal surfaces. We also prove a global uniqueness theorem that does not seem to be known in other situations.

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Ulrich Pinkall, Jonas Tervooren. 2017-06-20. A Weierstrass representation for 2D elasticity. https://arxiv.org/abs/1706.06387

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