Non-divergence harmonic maps

Details Non-divergence harmonic maps Non-divergence harmonic maps

2010-11-14

arxiv.org/abs/1011.3214v1

Mathematics

Differential Geometry

will appear in AMS Contemporary Math Series

Scientific paper

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.

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