Calculus of Variations and Geometric Measure Theory

A. Jevnikar - S. Kallel - A. Malchiodi

A topological join construction and the Toda system on compact surfaces of arbitrary genus

created by malchiodi on 18 Mar 2015
modified by jevnikar on 05 Nov 2015


Analysis and PDE

Inserted: 18 mar 2015
Last Updated: 5 nov 2015

Year: 2015


We consider a Toda system of Liouville equations on a compact surface $\Sigma$ which arises as a model for non-abelian Chern-Simons vortices.

For the first time the range of parameters $\rho_1 \in (4k\pi , 4(k+1)\pi)$, $k\in\mathbb{N}$, $\rho_2 \in (4\pi, 8\pi )$ is studied with a variational approach on surfaces with arbitrary genus. We provide a general existence result by means of a new improved Moser-Trudinger type inequality and introducing a topological join construction in order to describe the interaction of the two components.