Interaction of morphogens with geometry

Morphogen patterns are viewed as being affected by epithelial sheet geometry in early development. As the total area of the (closed) sheet changes, the changing geometry acts back in turn to change the morphogen pattern. A number of constraints are given on the functional form of the Gauss and Mean curvatures, considered as functions of the morphogen concentrations and their derivatives. It is shown that the constraints are sufficient to motivate a convincing dependence of the two curvatures on the morphogen concentrations.