  We describe how some differential geometric bifurcation problems can be
treated with the MATLAB continuation and bifurcation toolbox pde2path. The
basic setup consists in solving the PDEs for the normal displacement of an
immersed surface $X\subset\mathbb{R}^3$ and subsequent update of $X$ in each
continuation step, combined with bifurcation detection and localization,
followed by possible branch switching. Examples treated include some minimal
surfaces such as Enneper's surface and a Schwarz-P-family, some non-zero
constant mean curvature surfaces such as liquid bridges and nodoids, and some
4th order biomembrane models. In all of these we find interesting symmetry
breaking bifurcations. Some of these are (semi)analytically known and thus are
used as benchmarks.
