Asymptotic behaviour of solutions to the equation of constant mean curvature on a three-dimensional region

A first order differential inequality is derived for the cross-sectional energy flux of the solution to the equation of constant mean curvature defined on a three-dimensional prismatic cylinder of convex cross-section. Integration of the inequality yields estimates which are employed to prove for large values of the axial variable that the solution in measure either grows at least algebraically or decays at most exponentially to the lower dimensional cross-sectional solution. This result generalises that previously obtained by the authors for the corresponding two-dimensional problem. © 1996 Kluwer Academic Publishers.