%0 Journal Article %T Asymptotic behavior of Type III mean curvature flow on noncompact hypersurfaces %A Liang Cheng %A Natasa Sesum %J Mathematics %D 2014 %I arXiv %X In this paper, we introduce a monotonicity formula for the mean curvature flow which is related to self-expanders. Then we use the monotonicity to study the asymptotic behavior of Type III mean curvature flow on noncompact hypersurfaces. %U http://arxiv.org/abs/1403.0235v3