In this talk, we introduce a family of functionals approximating the conformally invariant Dirichlet n-energy of maps between two Riemannian manifolds $(M^n,g)$ and $(N,h)$, which admit critical points. Along the approximation process, these critical points may incur a bubbling phenomenon, due to the conformal invariance of the limit Dirichlet n-energy. We prove an energy identity result for this approximation, ensuring that no energy gets lost along the formation of bubbles, under a Struwe type entropy bound assumption. We then show that min-max problems for the n-energy are always solved by a "bubble tree" of n-harmonic maps. This is a joint work with T. Lamm.
NB:This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006