On the geometry of axisymmetric vesicles. (English) Zbl 1068.53052

Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 2nd international conference on geometry, integrability and quantization, Varna, Bulgaria, June 7–15, 2000. Sofia: Coral Press Scientific Publishing (ISBN 954-90618-2-5/pbk). 82-92 (2001).
A model of vesicles of the form of certain generalized Cassini ovals is given in terms of surfaces in \({\mathbb R}^3\) by a simple explicit parametrization depending on real parameters \(a\) and \(c\). Their form changes from that of a sphere to torocytes such that intermediate states resemble ellipsoids, discocytes and red blood cells as \(a\) runs between \(-c\) and \(c\). Expressions for the bending energy, for surface area, volume and other geometric quantities, suitable for experimentalists, are given.
For the entire collection see [Zbl 0957.00038].


53C80 Applications of global differential geometry to the sciences
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
74K15 Membranes