Proceedings of the International Conference on Geometry, Integrability and Quantization

Variational Problems In Elastic Theory of Biomembranes, Smectic-A Liquid Crystals, and Carbon Related Structures

Zhanchun Tu and Zhongcan Ou-Yang

Abstract

After a brief introduction to several variational problems in the study of shapes of thin structures, we deal with variational problems on two-dimensional surface in three-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

Article information

Source
Proceedings of the Seventh International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov and Manuel de León, eds. (Sofia: Softex, 2006), 237-248

Dates
First available in Project Euclid: 14 July 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1436909359

Digital Object Identifier
doi:10.7546/giq-7-2006-237-248

Mathematical Reviews number (MathSciNet)
MR2228376

Zentralblatt MATH identifier
1112.74018

Citation

Tu, Zhanchun; Ou-Yang, Zhongcan. Variational Problems In Elastic Theory of Biomembranes, Smectic-A Liquid Crystals, and Carbon Related Structures. Proceedings of the Seventh International Conference on Geometry, Integrability and Quantization, 237--248, Softex, Sofia, Bulgaria, 2006. doi:10.7546/giq-7-2006-237-248. https://projecteuclid.org/euclid.pgiq/1436909359


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