Sobolev spaces of isometric immersions of arbitrary dimension and codimension

Robert L. Jerrard, Mohammad Reza Pakzad

We prove the $C^1$ regularity and developability of $W^{2,p}$ isometric immersions of $n$-dimensional flat domains into ${\mathbb{R}}^{n+k}$ where $p\ge \min \{2k,n\}$. Another pa…