  In this paper, we prove that the infimum of the mean curvature is zero for a
translating solitons of hypersurface in $\re^{n+k}$. We give some conditions
under which a complete hypersurface translating soliton is stable. We show that
if the norm of its mean curvature is less than one, then the weighted volume
may have exponent growth. We also study the Dirichlet problem for graphic
translating solitons in higher codimensions.
