New solutions of the shape equation

The general shape equation describing the forms of vesicles is a highly nonlinear partial differential equation for which only a few explicit solutions are known. These solvable cases are briefly reviewed and a new analytical solution which represents the class of the constant mean curvature surfaces is described. Pearling states of the tubular fluid membranes can be explained as a continuous deformation preserving membrane mean curvature. Received 2 February 2002 / Received in final form 4 February 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: mladenov@obzor.bio21.bas.bg