Morse index estimates in min-max theorems (Q1826175)

Several results have been recently obtained about the possibility of determining the Morse index of a critical point found by a min-max approach. In this paper it is shown how, in correspondence with a given min-max class, one can find a critical point which satisfies some estimates (which depend on the dimension and the type of the class). The new information mainly consists in the possibility of localizing such a point and of using a suitable local compactness assumption. The answers given seem to be rather complete and to be obtained under weak assumptions.