An Analysis on the Shape Equation for Biconcave Axisymmetric Vesicles
  We study the conditions on the physical parameters in the Helfrich bending energy of lipid bilayer vesicles. Among embedded surfaces with a biconcave axisymmetric shape, the variation equation is analyzed in detail. This leads to simple conditions which guarantee the solution the information about the geometry. 
Thomas Kwok-keung Au and Tom Yau-heng Wan