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from Part III - Algebra, Topology, and Analysis in Origami
Published online by Cambridge University Press: 06 October 2020
In this chapter, tools from analysis are brought to bear on flat foldings of high-dimensional Euclidean space. The exposition follows the work of Dacorogna, Marcellini, and Paolini from 2008, who discovered that high-dimensional flat folding maps, which they call rigid maps, can be solutions to certain Dirichlet partial differential equations. This approach offers a different proof of the Recovery Theorem from Lawrence and Spingarn (1989), and the folding maps that result from Dirichlet problems can sometimes have crease patterns that exhibit interesting self-similarity.
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