  We present dynamic equations for two dimensional closed surfaces and
analytically solve it for some simplified cases. We derive final equations for
surface normal motions by two different ways. The solution of the equations of
motions in normal direction indicates that any closed, two dimensional,
homogeneous surface with time invariable surface energy density adopts constant
mean curvature shape when it comes in equilibrium with environment. As an
example, we apply the formalism to analyze equilibrium shapes of micelles and
explain why they adopt spherical, lamellar and cylindrical shapes. We show that
theoretical calculation for micellar optimal radius is in good agreement with
all atom simulations and experiments.

Biological Physics;Soft Condensed Matter