Harmonic maps with prescribed degrees on the boundary of an annulus and bifurcation of catenoids

Laurent Hauswirth, Rémy Rodiac

Let $A\subset {\mathbb{R}}^2$ be a smooth doubly connected domain. We consider the Dirichlet energy $E(u)={\int }_A|\nabla u{|}^2$, where $u:A\to \mathbb{C}$, and look for…