Abstract
The shape of vesicles with genus g=2, i.e., with two holes or two handles, is studied in the framework of curvature models. These vesicles exhibit a new phase which also persists for higher genus g>2. In this phase, the ground state of the vesicle is conformally degenerate even when the volume, the area, and the total mean curvature of the vesicle are kept constant. It is predicted that such vesicles undergo a new type of diffusive motion, termed conformal diffusion, which should be observable in experiments as pronounced shape fluctuations.
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