Non-divergence harmonic maps
Differential Geometry
2010-11-16 v1
Abstract
We describe work on solutions of certain non-divergence type and therefore non-variational elliptic and parabolic systems on manifolds. These systems include Hermitian and affine harmonics which should become useful tools for studying Hermitian and affine manifolds, resp. A key point is that in addition to the standard condition of nonpositive image curvature that is well known and understood in the theory of ordinary harmonic maps (which arise from a variational problem), here we also need in addition a global topological condition to guarantee the existence of solutions.
Cite
@article{arxiv.1011.3214,
title = {Non-divergence harmonic maps},
author = {Jürgen Jost and Fatma Muazzez Şimşir},
journal= {arXiv preprint arXiv:1011.3214},
year = {2010}
}
Comments
will appear in AMS Contemporary Math Series