On the Equivariant Implicit Function Theorem with Low Regularity and Applications to Geometric Variational Problems. Issue 1 (18th July 2014)

• Record Type: Journal Article
• Authors: Bettiol, Renato G.; Piccione, Paolo; Siciliano, Gaetano
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 58:Issue 1(2015)
• Page Start: 53
• Page End: 80
• Publication Date: 2014-07-18
• Subjects: implicit function theorem, -- geometric variational problems, -- CMC hypersurfaces, -- closed geodesics, -- harmonic maps; Primary 46T05, -- 47J07, -- 58C15, -- 58D19; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091513000631
• Languages: English
• ISSNs: 0013-0915

Abstract

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.