On Solutions for Singular Toda System on Riemann Surfaces with Boundary

Zhengni Hu

On Solutions for Singular Toda System on Riemann Surfaces with Boundary

Analysis of PDEs 2025-05-30 v3

Authors: Zhengni Hu

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.

Keywords

singular Toda system Riemann surface with boundary SU(3) linear source terms Euler characteristic Morse inequalities transversality theorem

Cite

@article{arxiv.2408.14979,
  title  = {On Solutions for Singular Toda System on Riemann Surfaces with Boundary},
  author = {Zhengni Hu},
  journal= {arXiv preprint arXiv:2408.14979},
  year   = {2025}
}

Comments

The Moser-Trudinger Inequality applied in this paper is incorrect. By the approach in this paper, it cannot obtain the general results

On Solutions for Singular Toda System on Riemann Surfaces with Boundary

Abstract

Keywords

Cite

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