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arXiv · 1302.0075

Rigidity and regularity of co-dimension one Sobolev isometric immersions

Zhuomin Liu·Mohammad Reza Pakzad
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Abstract

We prove the developability and $C^{1,1/2}$ regularity of $W^{2,2}$ isometric immersions of $n$-dimensional domains into $R^{n+1}$. As a conclusion we show that any such Sobolev isometry can be approximated by smooth isometries in the $W^{2,2}$ strong norm, provided the domain is $C^1$ and convex. Both results fail to be true if the Sobolev regularity is weaker than $W^{2,2}$.

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Zhuomin Liu, Mohammad Reza Pakzad. 2013-02-01. Rigidity and regularity of co-dimension one Sobolev isometric immersions. https://arxiv.org/abs/1302.0075

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