ASYMPTOTIC-BEHAVIOR OF SOLUTIONS TO THE EQUATION OF CONSTANT MEAN-CURVATURE ON A 3-DIMENSIONAL REGION

A first order differential inequality is derived for the cross-section al energy flux of the solution to the equation of constant mean curvat ure defined on a three-dimensional prismatic cylinder of convex cross- section. Integration of the inequality yields estimates which are empl oyed to prove for large values of the axial variable that the solution in measure either grows at least algebraically or decays al most expo nentially to the lower dimensional cross-sectional solution. This resu lt generalises that previously obtained by the authors for the corresp onding two-dimensional problem.