𝐶^{1,1-𝜖} isometric embeddings

Abstract

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 h -principle for isometric embeddings in the class C 1 , 1 − ε C^{1,1-\varepsilon } for n n -dimensional manifolds in codimension 1 2 n ( n + 1 ) \frac {1}{2}n(n+1) .