  After a brief introduction to several variational problems in the study of
shapes of thin thickness structures, we deal with variational problems on
2-dimensional surface in 3-dimensional Euclidian space by using exterior
differential forms. The morphological problems of lipid bilayers and
stabilities of cell membranes are also discussed. The key point is that the
first and the second order variations of the free energy determine equilibrium
shapes and mechanical stabilities of structures.
