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Harmonic maps on complete manifolds
1.  Department of Mathematics, Southwest Missouri State University 
2.  Department of Applied Mathematics, University of Colorado at Boulder 
Our condition are: The Ricci curvature of M is bounded from below by a negative constant, M admits a positive Green’s function and
$ \int_M G(x, y)\tau(h(y))dV_y $ is bounded on each compact subset. $\qquad$ (1)
Here $\tau(h(x))$ is the tension field of the initial data $h(x)$.
Condition (1) is somewhat sharp as is shown by examples in the paper.
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