论文标题
统治会导致$ n $ -fuchsian纤维在Higgs束的模量空间中
Domination results in $n$-Fuchsian fibers in the moduli space of Higgs bundles
论文作者
论文摘要
在本文中，我们显示了有关Hitchin纤维化的一些统治结果，主要关注$ n $ fuchsian纤维。更准确地说，我们显示了$ n $ fuchsian表示相关的谐波图的能量密度，在同一hitchin纤维中占主导地位，这意味着拓扑不变性的统治：翻译长度光谱和熵。作为能量密度支配的应用，我们获得了某些产物Riemannian（或伪里曼尼亚语）歧管中的模化最小（或最大）表面的存在和独特性。我们的证明是基于建立代数不平等，将NESS的GIT定理推广到Nilpotent Orbits到一般轨道。
In this article, we show some domination results on the Hitchin fibration, mainly focusing on the $n$-Fuchsian fibers. More precisely, we show the energy density of associated harmonic map of an $n$-Fuchsian representation dominates the ones of all other representations in the same Hitchin fiber, which implies the domination of topological invariants: translation length spectrum and entropy. As applications of the energy density domination results, we obtain the existence and uniqueness of equivariant minimal (or maximal) surfaces in certain product Riemannian (or pseudo-Riemannian) manifold. Our proof is based on establishing an algebraic inequality generalizing a GIT theorem of Ness on the nilpotent orbits to general orbits.
