# 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

[BibTeX]

Analysis and PDE

Inserted: 18 mar 2015
Last Updated: 5 nov 2015

Year: 2015

Abstract:

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.