Solutions of the torsion problem with many critical points in Riemannian manifolds

Given a complete Riemannian manifold (M,g) I will prove that, for any point p in M and for any integer n>2, there exists a family of sets containing p and a family of solutions to the torsion problem that admits at least n maximum points. Moreover the domains are close to be convex (in a suitable sense). The proof relies on similar results in R^d, for d>3.
The talk is based on past and ongoing results involving M. Grossi and A. Enciso.