Eigenvalue optimisation and n-harmonic maps

Abstract: On a surface, eigenvalue optimisation with respect to the metric leads to minimal surfaces (in a sphere for Laplace eigenvalue, free boundary minimal in a ball for Steklov ones). When we restrict the optimisation problem to a conformal class, the corresponding object we obtain are harmonic maps. I will discuss generalisation to higher dimension of these results and how n-harmonic maps play a crucial role in it.

analysis of PDEsclassical analysis and ODEsfunctional analysisprobabilityspectral theory

Audience: researchers in the discipline

Quebec Analysis and Related Fields Graduate Seminar