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arXiv · 1503.05524

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

Aleks Jevnikar·Sadok Kallel·Andrea Malchiodi
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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.

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Aleks Jevnikar, Sadok Kallel, Andrea Malchiodi. 2015-03-18. A topological join construction and the Toda system on compact surfaces of arbitrary genus. https://doi.org/10.2140/apde.2015.8.1963

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