论文标题
TODA方程和循环希格斯的完整溶液在非紧密表面上
Complete solutions of Toda equations and cyclic Higgs bundles over non-compact surfaces
论文作者
论文摘要
在带有全态$ r $ $ differential的黎曼表面上，一个人可以自然地定义toda方程和带有分级的循环higgs束。 TODA方程的解决方案等效于谐波束的谐波度量，该指标是正交的。在这里，我们专注于一般的非紧缩Riemann表面，其$ r $ diffentiential不一定是无穷大的meromormorphic。我们介绍了TODA方程的完整解决方案的概念，并通过对TODA方程和谐波束的技术来证明完整解决方案的存在和唯一性。此外，我们显示了完整解决方案的一些定量估计。
On a Riemann surface with a holomorphic $r$-differential, one can naturally define a Toda equation and a cyclic Higgs bundle with a grading. A solution of the Toda equation is equivalent to a harmonic metric of the Higgs bundle for which the grading is orthogonal. Here we focus on a general non-compact Riemann surface with an $r$-differential which is not necessarily meromorphic at infinity. We introduce the notion of complete solution of the Toda equation, and we prove the existence and uniqueness of a complete solution by using techniques for both Toda equations and harmonic bundles. Moreover, we show some quantitative estimates of the complete solution.
