  We introduce a general scheme that permits to generate successive min-max
problems for producing critical points of higher and higher indices to
Palais-Smale Functionals in normal Banach manifolds equipped with complete
Finsler structures. We call the resulting tree of minmax problems a minmax
hierarchy. We give several examples and in particular we explain how to
implement this scheme in the framework of the viscosity method introduced by
the author some years ago in order to give a new proof of the Willmore
conjecture after the famous result by Marques and Neves.
