A Mathematical Examination of Squeezing and Stretching of Spherical Vesicles

Abstract

The geometry of a few simple models closely related to the Cole’s and Yoneda’s experiments are studied in some detail. Their principal differences are through the boundary conditions at the points where the membranes detach themselves from the compressing planes. Mathematically this affect the equilibrium configurations as in all these cases the mean curvature suffers a discontinuity while this is not so for the tangent vector. A new parametrization of the Delaunay’s nodoids is derived.