On the Local Solvability of Darboux's Equation
Analysis of PDEs
2010-03-12 v1 Differential Geometry
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.
Cite
@article{arxiv.1003.2240,
title = {On the Local Solvability of Darboux's Equation},
author = {Marcus A. Khuri},
journal= {arXiv preprint arXiv:1003.2240},
year = {2010}
}