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

Authors
Type
Preprint
Publication Date
Mar 18, 2015
Submission Date
Mar 18, 2015
Identifiers
arXiv ID: 1503.05524
Source
arXiv
We consider a Toda system of Liouville equations defined on a compact surface 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.