The Morse property for functions of Kirchhoff-Routh path type (Q2321746)

This article discusses Morse property for functions \[ f_\Omega(x_1,x_2,\dots,x_N)=f(x_1,x_2,\dots,x_N)-\sum_{j,k=1}^N\lambda_j\lambda_kH_\Omega(x_j,x_k), \] where \(\Omega\subset \mathbb{R}^n\) is a bounded domain, \(f\) is a \(C^2\) function defined on a domain in \(\mathbb{R}^{nN}\) and \(H_\Omega\) is the regular part of the Green function on \(\Omega\) object to the Dirichlet condition. The authors establish that for generic domains \(\Omega\), the function \(f_\Omega\) is a Morse function, in the sense that all of its critical points are non-degenerate.