-
A general existence proof for non-linear elliptic equations in semi-Riemannian spaces
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 131, Number 6, December 2009
- pp. 1569-1588
- 10.1353/ajm.0.0078
- Article
- Additional Information
- Purchase/rental options available:
We present a general existence proof for a wide class of non-linear
elliptic equations which can be applied to problems with barrier
conditions without specifying any assumptions guaranteeing the
uniqueness or local uniqueness of particular solutions.
As an application we prove the existence of closed
hypersurfaces with curvature prescribed in the tangent bundle of an
ambient Riemannian manifold $N$ without supposing any sign condition on
the sectional curvatures $K_N$. A curvature flow wouldn't work in this
situation, neither the method of successive approximation.