Unstretchable thin elastic plates such as paper can be modelled as intrinsically flat W 2,2 isometric immersions from a domain in ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4900/nonab9245ieqn1.gif] {${\mathbb{R}}^{2}$} into ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4900/nonab9245ieqn2.gif] {${\mathbb{R}}^{3}$} . In previous work it has been shown that if such an isometric immersion minimizes the elastic energy, then it is smooth away from a singular set consisting of three different subsets. In the present paper, we show that each of these singular subsets can indeed occur and that regularity may indeed fail there.

中文翻译：

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关于静态等距变形的奇异性

不可拉伸的薄弹性板（例如纸）可以建模为来自## IMG ## [http://ej.iop.org/images/0951-7715/33/9/4900 /nonab9245ieqn1.gif] {$ {\ mathbb {R}} ^ {2} $}到## IMG ## [http://ej.iop.org/images/0951-7715/33/9/4900/nonab9245ieqn2 .gif] {$ {\ mathbb {R}} ^ {3} $}。在以前的工作中，已经表明，如果这样的等距浸入最小化了弹性能，那么它将远离包含三个不同子集的奇异集而变得平滑。在本文中，我们证明了这些奇异子集的每一个确实可以发生，并且规则性确实可能在此失败。