On the Local Solvability of Darboux's Equation

Abstract

We reduce the question of local nonsolvability of the Darboux equation, and hence of the isometric embedding problem for surfaces, to the local nonsolvability of a simple linear equation whose type is explicitly determined by the Gaussian curvature.

Cited by in corpus (1)

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