Variational Problems in Elastic Theory of Biomembranes, Smectic-a Liquid Crystals, and Carbon Related Structures
نویسنده
چکیده
Abstract. After a brief introduction to several variational problems in the study of shapes of thin structures, we deal with variational problems on 2dimensional surface in 3-dimensional Euclidian space by using exterior differential forms and the moving frame method. 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.
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