Minimality of degree-one Ginzburg-Landau vortex in the unit ball

In this talk, we will focus on the standard Ginzburg-Landau functional for N-dimensional maps defined in the unit ball that are equal to the identity on the boundary. A special critical point is the so-called degree-one vortex map given by the identity map multiplied with a scalar radial profile. We will prove the minimality of this solution and also discuss about the uniqueness result. This is a joint work with L. Nguyen, V. Slastikov and A. Zarnescu.