On the equivariant implicit function theorem with low regularity and applications to geometric variational problems
Differential Geometry
2015-02-10 v3
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.
Cite
@article{arxiv.1009.5721,
title = {On the equivariant implicit function theorem with low regularity and applications to geometric variational problems},
author = {Renato G. Bettiol and Paolo Piccione and Gaetano Siciliano},
journal= {arXiv preprint arXiv:1009.5721},
year = {2015}
}
Comments
LaTeX2e, 23 pages, revised version. To appear in Proc. Edinb. Math. Soc