On the strong maximum principle and the large time behavior of generalizedmean curvature flow with the Neumann boundary condition

A generalized mean curvature now is considered in a cylindrical domain unde r the right angle boundary condition. Its large time behavior is studied by analyzing the level set equation of the now when the initial hypersurface is nor necessarily graph-like. For a convex domain it is shown that the sol ution of the level set equation converges to a function whose level sets ar e perpendicular to the lateral boundary of the domain as time tends to infi nity (when the initial data is constant outside some bounded set). For this purpose a version of the strong maximum principle is established for the l evel set minimal surface equation although the equation is degenerate. (C) 1999 Academic Press.