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On the Local Isometric Embedding in R^3 of Surfaces with Gaussian Curvature of Mixed Sign (1009.6214v1)
Published 30 Sep 2010 in math.AP and math.DG
Abstract: We study the old problem of isometrically embedding a 2-dimensional Riemannian manifold into Euclidean 3-space. It is shown that if the Gaussian curvature vanishes to finite order and its zero set consists of two Lipschitz curves intersecting transversely at a point, then local sufficiently smooth isometric embeddings exist.
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