Abstract: The Local Isometric Embedding Problem is an open problem in surface theory, and pertains to whether or not an abstract surface can be locally realized as a graph in ${\Bbb R}^3$. We describe a solution wherein any Riemannian surface can be locally isometrically embedded into ${\Bbb R}^4$ as a graph over a surface of constant Gaussian curvature in ${\Bbb R}^3$. This result may provide insight into the open problem of embedding surfaces of non-identically zero curvature into ${\Bbb R}^3$.
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