ON THE EQUIVARIANT IMPLICIT FUNCTION THEOREM WITH LOW REGULARITY AND APPLICATIONS TO GEOMETRIC VARIATIONAL PROBLEMS

Author(s)

Bettiol, Renato G. ^[1] ; Piccione, Paolo ^[2] ; Siciliano, Gaetano ^[2]

Affiliation

^[1] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 - USA

^[2] Univ Sao Paulo, Dept Matemat, BR-05508090 Sao Paulo, SP - Brazil

• Document type: Journal article
• Source: PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY; v. 58, n. 1, p. 53-80, FEB 2015.
• Web of Science Citations: 2

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. (AU)

• FAPESP's process: 10/00068-6 - Variational and topologucal methods for field equations
• Grantee: Gaetano Siciliano
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 11/21362-2 - Group actions, submanifold theory and global analysis in Riemannian and pseudo-Riemannian geometry
• Grantee: Paolo Piccione
• Support Opportunities: Research Projects - Thematic Grants