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

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

2010-09-30

arxiv.org/abs/1009.6214v1

Mathematics

Analysis of PDEs

Comm. Anal. Geom., to appear, 47 pages

Scientific paper

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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