任意亏格紧致曲面上的拓扑连接构造与Toda系
A topological join construction and the Toda system on compact surfaces of arbitrary genus
摘要：
我们考虑一个Toda系统的刘维尔方程定义在一个紧凑的表面上出现的非阿贝尔陈-西蒙斯涡的模型。首次用变分方法研究了任意亏格曲面上参数$ρ_1 \in (4kπ, 4(k+1)π)$，$k \in \mathbb{N}$，$ρ_2 \in (4π, 8π)$的取值范围.我们通过一个新的改进的Moser-Trudinger型不等式和引入拓扑连接构造来描述两个分量的相互作用，给出了一个普遍的存在性结果.
英文摘要：
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 $ρ_1 \in (4kπ, 4(k+1)π)$, $k \in \mathbb{N}$, $ρ_2 \in (4π, 8π)$ 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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