Abstract
We prove an extension of a celebrated equivariant bifurcation result of J. Smoller and A. Wasserman [21], 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.
Mathematics Subject Classification (2010).58E07, 58E09, 46T05, 58D19, 53A10.
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Bettiol, R.G., Piccione, P., Siciliano, G. (2014). Equivariant Bifurcation in Geometric Variational Problems. In: de Figueiredo, D., do Ó, J., Tomei, C. (eds) Analysis and Topology in Nonlinear Differential Equations. Progress in Nonlinear Differential Equations and Their Applications, vol 85. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-04214-5_6
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DOI: https://doi.org/10.1007/978-3-319-04214-5_6
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