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A general existence proof for non-linear elliptic equations in semi-Riemannian spaces

Claus Gerhardt Ruprecht-Karls-Universität, Institut für Angewandte Mathematik

Differential Geometry mathscidoc:1610.10001

Amer.J. Math., 131, (6), 1569 - 1588, 2009
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.
Semi-Riemannian manifolds, non-linear elliptic equations, existence proof, curvature functions of class $(K^*)$, hypersurfaces with prescribed curvature
[ Download ] [ 2016-10-02 03:35:38 uploaded by gerhardt ] [ 1715 downloads ] [ 0 comments ] [ Cited by 1 ] 
@inproceedings{claus2009a,
  title={A general existence proof for  non-linear elliptic equations in semi-Riemannian spaces},
  author={Claus Gerhardt},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161002033538270043059},
  booktitle={Amer.J. Math.},
  volume={131},
  number={6},
  pages={1569 - 1588},
  year={2009},
}
Claus Gerhardt. A general existence proof for non-linear elliptic equations in semi-Riemannian spaces. 2009. Vol. 131. In Amer.J. Math.. pp.1569 - 1588. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161002033538270043059.
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