English

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.

Keywords

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}
}