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cmc hypersurfaces

Proceedings of the Edinburgh Mathematical Society (1)

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On the Equivariant Implicit Function Theorem with Low Regularity and Applications to Geometric Variational Problems
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Renato G. Bettiol, Paolo Piccione, Gaetano Siciliano
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 58 / Issue 1 / February 2015

Published online by Cambridge University Press:

18 July 2014, pp. 53-80
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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.