$C^{1,1-\epsilon }$ Isometric embeddings

In this paper we use the convex integration technique enhanced by an extra iteration originally due to Källén and revisited by Kröner to provide a local $h$-principle for isometric embeddings in the class $C^{1,1-\epsilon }$ for $n$-dimensional manifolds in codimension $\frac{1}{2}n(n+1)$.