Variational methods in the presence of symmetry

Abstract

The purpose of this paper is to survey and to provide a unified framework to connect a diverse group of results, currently scattered in the literature, that can be usefully viewed as consequences of applying variational methods to problems involving symmetry. Here, variational methods refer to mathematical treatment by way of constructing an appropriate action function whose critical points—or saddle points—correspond to or contain the desired solutions.

Keywords

• variational methods
• convex analysis
• symmetry
• group action