Stability Property and Dirichlet Problem for Translating Solitons

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