Equivariant bifurcation in geometric variational problems
Differential Geometry
2014-07-17 v1
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.
Cite
@article{arxiv.1308.3268,
title = {Equivariant bifurcation in geometric variational problems},
author = {Renato G. Bettiol and Paolo Piccione and Gaetano Siciliano},
journal= {arXiv preprint arXiv:1308.3268},
year = {2014}
}
Comments
LaTeX2e, 27 pages, 2 figures. To appear in Proceedings of the 9th WNLDE (Birkhauser)