Given an immersion of a surface into the euclidean $3$ space, the Willmore functional is defined as the $L^2$ norm of the mean curvature. If we consider immersions in a Riemannian manifold there are many possible generalizations of the Willmore functional; in the seminar we will speak about these generalizations and study the existence of minimizers and critical points of the corresponding functionals under curvature or topological conditions on the ambient manifold. The topic has links with general relativity, string theory, biology, nonlinear elasticity theory etc.
