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 $ ho_1 in (4kpi , 4(k+1)pi)$, $k in mathbb{N}$, $ ho_2 in (4pi, 8pi )$ 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.

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

MALCHIODI, ANDREA
2015

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 $ ho_1 in (4kpi , 4(k+1)pi)$, $k in mathbb{N}$, $ ho_2 in (4pi, 8pi )$ 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.
Settore MAT/05 - Analisi Matematica
Geometric PDEs, Variational Methods, Min-max Schemes
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11384/57120
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