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arXiv · 1009.5721

On the equivariant implicit function theorem with low regularity and applications to geometric variational problems

Renato G. Bettiol·Paolo Piccione·Gaetano Siciliano
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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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Renato G. Bettiol, Paolo Piccione, Gaetano Siciliano. 2013-01-29. On the equivariant implicit function theorem with low regularity and applications to geometric variational problems. https://doi.org/10.1017/s0013091513000631

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