OVERVIEW OF THE STUDY OF COMPLEX SHAPES OF FLUID MEMBRANES, THE HELFRICH MODEL AND NEW APPLICATIONS

Some progresses in shape problems following the Helfrich model are reported. Based on the Helfrich model, we have predicted not only the exact solution for discoidal shape of red blood cells but also a special kind of toroidal vesicle with the ratio of two generation radii being root 2. The Helfrich model can also be extended to investigate the complex structures in other soft matters such as the formation of focal conic domains in smectic liquid crystal, the tube-to-sphere transition in peptide nanostructures, and icosahedral configuration of small virus capsids.