A PHRAGMEN-LINDELOF PRINCIPLE FOR THE EQUATION OF A SURFACE OF CONSTANT MEAN-CURVATURE

This paper studies the surface of constant mean curvature on a semi-in finite strip, and shows by means of a first-order differential inequal ity that the solution in a given measure either becomes asymptotically unbounded at least to polynomial order, or decays at most exponential ly to the solution of an associated one-dimensional problem. A proof i s also presented for uniqueness in the class of functions having bound ed gradient and subject to specified growth conditions for large value s of the longitudinal distance. Extensions of these results to the who le strip and to more general types of equations are also described.