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On the Equivariant Implicit Function Theorem with Low Regularity and Applications to Geometric Variational Problems
Published online by Cambridge University Press: 18 July 2014
Abstract
We prove an implicit function theorem for functions on infinite-dimensional Banach manifolds, invariant under the (local) action of a finite-dimensional Lie group. Motivated by some geometric variational problems, we consider group actions that are not necessarily differentiable everywhere, but only on some dense subset. Applications are discussed in the context of harmonic maps, closed (pseudo-) Riemannian geodesics and constant mean curvature hypersurfaces.
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- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 58 , Issue 1 , February 2015 , pp. 53 - 80
- Copyright
- Copyright © Edinburgh Mathematical Society 2015
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