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

Abstract

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.

References in corpus (1)

• Existence and multiplicity result for the singular Toda system

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