Equivariant bifurcation in geometric variational problems

Abstract

We prove an extension of a celebrated equivariant bifurcation result of J. Smoller and A. Wasserman, in an abstract framework for geometric variational problems. With this purpose, we prove a slice theorem for continuous affine actions of a (finite-dimensional) Lie group on Banach manifolds. As an application, we discuss equivariant bifurcation of constant mean curvature hypersurfaces, providing a few concrete examples and counter-examples.Comment: LaTeX2e, 27 pages, 2 figures. To appear in Proceedings of the 9th WNLDE (Birkhauser