Vanishing elastic energy implies subsequence convergence to an isometric immersion for codimension-1 maps into complete manifolds.
Lee.Introduction to Riemannian manifolds, volume 176 ofGraduate Texts in Mathematics
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Rigidity of codimension-1 isometric immersions in complete manifolds
Vanishing elastic energy implies subsequence convergence to an isometric immersion for codimension-1 maps into complete manifolds.