In this paper, we prove a monotonicity formula and some Bernstein type results for translating solitons of hypersurfaces in $\re^{ n+1}$, giving some conditions under which a trantranslating soliton is a hyperplane. We also show a gap theorem for the translating soliton of hypersurfaces in $R^{ n+k}$, namely, if the $L^n$ norm of the second fundamental form of the soliton is small enough, then it is a hyperplane.
Categories: math.DG math.AP