Differential Geometry, Lie Theory and Low-Dimensional Topology, Melbourne, Australia, 2016

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Details of talk

TitleStability and bifurcation for surfaces with constant mean curvature
PresenterMiyuki Koiso (Kyushu University)
Author(s)Prof Miyuki Koiso
Sessionn/a
Time
Abstract


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.