Cartan's and Gauss's equations and rigidity theorems for isometric embeddings in low Sobolev regularity

Isaac Newell, Luc Nguyen

Let $\{{\eta }^i{\}}_{i=1}^2$ be a an orthonormal coframe on a domain $U$ on a smooth surface $(\Sigma ,g)$. When ${\eta }^i$ is smooth, it is well-known that there is a unique connection 1-form $\omega$ v…