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arXiv · 2408.14979

On Solutions for Singular Toda System on Riemann Surfaces with Boundary

Zhengni Hu
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Abstract

This paper studies solutions to a singular $SU(3)$ Toda system with linear source terms on a compact Riemann surface $\Sigma$ with smooth boundaries $\partial\Sigma$. We establish the existence of solutions when the parameters are not critical, assuming that Euler characteristic $\chi(\Sigma)<1$ via analyzing the sublevels. Furthermore, we find a sufficient condition that ensures multiple solutions for generic potentials by Morse inequalities and a transversality theorem.

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Zhengni Hu. 2024-08-27. On Solutions for Singular Toda System on Riemann Surfaces with Boundary. https://arxiv.org/abs/2408.14979

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