A note on the asymptotic behavior of parabolic monge-ampère equations on riemannian manifolds

We study the asymptotic behavior of the parabolic monge-ampère equation ∂(x,t)/∂t=log (det(g(x)+hess(x,t))/detg(x))-(x,t) in ×(0,∞),(x,0)=0(x) in,where is a compact complete riemannian manifold,is a positive real parameter,and 0(x): is a smooth function. we show a meaningful asymptotic result which is more general than those in huisken,1997. © 2013 qiang ru.