Minimal submanifolds in infinite dimensions (Q2771411)

The difficulty arising in the study of minimal submanifolds in infinite dimensional manifolds is that the mean curvature, defined as usual by the trace of the shape operator, may not be finite. Further, the volume of the submanifold may not be defined. In this article, the authors use zeta-function regularizations of Ray-Singer to study submanifolds in infinite dimensional manifolds. They show several interesting cases in which the mean curvature is defined. They also prove the existence of minimal gauge orbits of flat \(SU(2)\)-connections over certain Seifert fibered homology 3-spheres.NEWLINENEWLINEFor the entire collection see [Zbl 0953.00036].