Variational Problems in Elastic Theory of Biomembranes, Smectic-a Liquid Crystals, and Carbon Related Structures

摘要

After a brief introduction to several variational problems in the study ofshapes of thin thickness structures, we deal with variational problems on2-dimensional surface in 3-dimensional Euclidian space by using exteriordifferential forms. The morphological problems of lipid bilayers andstabilities of cell membranes are also discussed. The key point is that thefirst and the second order variations of the free energy determine equilibriumshapes and mechanical stabilities of structures.