Existence and regularity of isometries

Michael Taylor
2006 Transactions of the American Mathematical Society  
We use local harmonic coordinates to establish sharp results on the regularity of isometric maps between Riemannian manifolds whose metric tensors have limited regularity (e.g., are Hölder continuous). We also discuss the issue of local flatness and of local isometric embedding with given first and second fundamental form, in the context of limited smoothness.
doi:10.1090/s0002-9947-06-04090-6 fatcat:yd4xod3xrrdizoenhtpi5e5m2u