Gradient Estimate For Harmonic Maps From Smooth Metric Measure Spaces And Its Applications

In this paper,we mainly studied 0-harmonic maps from metric measure spaces(M,g,e-? dv)to Riemannian manifold(N,h)with nonpositive sectional curvature,We proved the gradient estimate of 0-harmonic maps under appropriate conditions,we also gave the existence of the Liouville type theorem with the help of the gradient estimate.