Denote by ${\eufm M}(\Sigma)$ the space of hyperbolic metrics on a closed, orientable surface $\Sigma$ and by ${\eufm M}(M)$ the space of negatively curved Riemannian metrics on a closed, orientable 3-manifold $M$. We show that the set of metrics for which the corresponding harmonic map is in Whitney's general position is an open, dense, and connected subset of ${\eufm M}(\Sigma)\times {\eufm M}(M)$. The main application of this result is the proof of the Simple Loop Theorem for hyperbolic 3-manifolds. Consequences regarding minimal surfaces will be mentioned.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444