$C^{1,1-ε}$ Isometric embeddings

Abstract

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