Bifurcation of extremals near the singularities of a multidimensional plate (Q1390404)

The author studies the stationary points of \(V^{(4)}+ V^{(3)}+ V^{(2)}\) \((V^{(n)}\) a homogeneous polynomial of degree \(n\) on an \(m\)-dimensional vector space) for a fixed positive \(V^{(4)}\). He gives some formulas concerning the occurring bif-layouts \((l_0,l_1,\dots,l_m)\), where \(l_k\) is the number of Morse stationary points of index \(k\), including a complete list of them when \(m=2\). The results are used to study the bifurcations of a min-singularity which is an \(m\)-dimensional plate.