In this paper, we prove the existence of an isometric embedding near the origin in R3 of a two-dimensional metric with nonpositive Gaussian curvature. The Gaussian curvature can be allowed to be highly degenerate near the origin. Through the Gauss-Codazzi equations, the embedding problem is reduced to a 2 × 2 system of the first order derivaties and is solved via the method of Nash-Moser-Hörmander iterative scheme.
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