Min–max schemes for SU(3) Toda systems

Abstract

This paper surveys some recent results on Toda systems of Liouville equations. These systems model self-dual non-abelian ChernSimons vortices, and arise in the study of holomorphic curves. Suitable min-max schemes are employed, leading to existence of solutions in several situations. We will use in particular properties about concentration of exponential functions in order to describe low-energy levels of the Euler-Lagrange energy.Mathematics Subject Classification. 35B33, 35J35, 53A30, 53C21.