On singularities of stationary isometric deformations

Abstract

Abstract Unstretchable thin elastic plates such as paper can be modelled as intrinsically flat W 2,2 isometric immersions from a domain in R 2 into 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.