On the Local Isometric Embedding in $R^3$ of Surfaces with Zero Sets of Gaussian Curvature Forming Cusp Domains

Abstract

We study the problem of isometrically embedding a two-dimensional Riemannian manifold into Euclidean three-space. It is shown that if Gaussian curvature vanishes to finite order and its zero set consists of two smooth curves tangent at a point, then local sufficiently smooth isometric embedding exists.

arXiv admin note: text overlap with arXiv:1009.6214 by other authors

References in corpus (3)

• Isometric embedding via strongly symmetric positive systems
• Local Solvability of a Class of Degenerate Monge-Ampere Equations and Applications to Geometry
• On the Local Solvability of Darboux's Equation

Cited by in corpus (1)

• On the local isometric embedding of trapped surfaces into three-dimensional Riemannian manifolds