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.

LaTeX2e, 27 pages, 2 figures. To appear in Proceedings of the 9th WNLDE (Birkhauser)

References in corpus (2)

• Multiplicity of solutions to the Yamabe problem on collapsing Riemannian submersions
• Delaunay-type hypersurfaces in cohomogeneity one manifolds

Cited by in corpus (5)

• Delaunay-type hypersurfaces in cohomogeneity one manifolds
• Full Laplace spectrum of distance spheres in symmetric spaces of rank one
• Parameterized splitting theorems and bifurcations for potential operators
• Parameterized splitting theorems and bifurcations for potential operators, Part I: Abstract theory
• Parameterized splitting theorems and bifurcations for potential operators, Part II: Applications to quasi-linear elliptic equations and systems