平面上指数衰减 Seiberg-Witten 旋涡方程解的存在性
偏微分方程分析
2026-05-08 v3 数学物理
复变函数
微分几何
math.MP
摘要
Clifford Taubes 证明了 Yang-Mills-Higgs 泛函变分方程在平面上的模空间非空，其元素对应于“旋涡”。受此结果启发，本文表明 Seiberg-Witten 方程在平面上的 Hitchin 型维数约化模空间包含既指数衰减解又多项式增长解。
引用
@article{arxiv.2406.20043,
title = {Existence of Solutions to the Seiberg-Witten Vortex Equations with Exponential Decay on the Plane},
author = {William L. Blair and Minh Lam Nguyen},
journal= {arXiv preprint arXiv:2406.20043},
year = {2026}
}
备注
35 pages, comments are welcome! Fix typos, make revisions. In particular, the previously considered Kazdan-Warner equation is no longer relevant. In its place, we study an existence result for a singular sinh-Gordon equation