Isometric embedding via strongly symmetric positive systems

@article{Chen2015IsometricEV,
  title={Isometric embedding via strongly symmetric positive systems},
  author={Gui-Qiang G. Chen and Jeanne Nielsen Clelland and Marshall Slemrod and Dehua Wang and Deane Yang},
  journal={arXiv: Differential Geometry},
  year={2015}
}
We give a new proof for the local existence of a smooth isometric embedding of a smooth $3$-dimensional Riemannian manifold with nonzero Riemannian curvature tensor into $6$-dimensional Euclidean space. Our proof avoids the sophisticated arguments via microlocal analysis used in earlier proofs. In Part 1, we introduce a new type of system of partial differential equations, which is not one of the standard types (elliptic, hyperbolic, parabolic) but satisfies a property called strong symmetric… 
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