On the local isometric embedding in ℝ3of surfaces with zero sets of Gaussian curvature forming cusp domains
Tsung-Yin Lin · Communications in Partial Differential Equations · 2016
We study the problem of isometrically embedding a two-dimensional Riemannian manifold into Euclidean three-space. It is shown that if the Gaussian curvature vanishes to finite order and its zero set consists of two smooth curves tangent at a point, then local sufficiently smooth isometric embeddings exist.