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We study the old problem of isometrically embedding a 2-dimensionalRiemannian manifold into Euclidean 3-space. It is shown that if the Gaussiancurvature vanishes to finite order and its zero set consists of two Lipschitzcurves intersecting transversely at a point, then local sufficiently smoothisometric embeddings exist.

On the Local Isometric Embedding in R^3 of Surfaces with Gaussian Curvature of Mixed Sign