Properties of surfaces with spontaneous curvature

22.11.2023 11:30 - 13:00

Christian Scharrer (U Bonn)

    In the early 70s, Wolfgang Helfrich proposed to model lipid bilayer cell membranes as optimal shapes with regard to the L^2-deficit of their mean curvature to a given constant called spontaneous curvature. A typical problem in mathematics is then to investigate whether such optimal shapes do exist. In this talk I will give an overview about some recent results, basic properties, and open questions starting with the special case of zero spontaneous curvature. Several examples will be presented to indicate difficulties such as lower semi-continuity for nonzero spontaneous curvature.


T. Körber, A. Molchanova, F. Rupp


BZ 2, 2. OG., OMP 1