Functional-operator method for investigation of bifurcations in the equivariant Plateau problem (Q1390407)

The paper is devoted to the study of invariant minimal submanifolds in \({\mathbb R}^{m+n+2}\) with invariant prescribed boundaries. The symmetry group is the product of two compact orthogonal groups, \(SO(m+1)\times SO(n+1)\). Following earlier papers by the author [see, e.g., \textit{A. Yu. Borisovich}, Adv. Sov. Math. 15, 287-330 (1993; Zbl 0789.58024)], the problem is transformed to an equation in the realm of operators on Banach spaces. A series of assumptions allows then to combine several functional-analytical methods in order to obtain existence results on bifurcations of minimal submanifolds. Finally, the possible applications are illustrated on bifurcations of cones in higher dimensions.