|Title||Stability and bifurcation for surfaces with constant mean curvature|
|Presenter||Miyuki Koiso (Kyushu University)|
|Author(s)||Prof Miyuki Koiso|
A surface with constant mean curvature (CMC surface) is an equilibrium surface of the area functional among surfaces which enclose the same volume (and satisfy given boundary conditions). A CMC surface is said to be stable if the second variation of the area is nonnegative for all volume-preserving variations. In this talk we first give criteria for stability of CMC surfaces in the three-dimensional euclidean space. We also give a sufficient condition for the existence of smooth bifurcation branches of fixed boundary CMC surfaces, and we discuss stability/instability issues for the surfaces in bifurcating branches. By applying our theory, we determine the stability/instability of some explicit examples of CMC surfaces.