论文标题
与希钦表示相关的teichmüller空间上的能量的严格多数
Strict plurisubharmonicity of the energy on Teichmüller space associated to Hitchin representations
论文作者
论文摘要
令$σ$为属的闭合表面至少两个，$ρ\colonπ_1（σ）\ to g $ a hitchin表示为$ g = \ text {psl}（n，n，\ m asthbb {r}）$，$ \ $ \ text {psp} $ \ text {g} _2 $。我们考虑了$σ$的TeichMüller空间上的能量功能$ E $，该$ $ \ Mathcal {t}（σ）$分配给每个点的$ \ Mathcal {t}（σ）$相关的$ρ$ Equivariant谐波映射的能量。本文的主要结果是$ e $严格是plurisubharmonic。作为推论，我们获得了$ 3 \ cdot \ text {enus}（σ）-3 $的上限，在能量功能的任何临界点的索引上。
Let $Σ$ be a closed surface of genus least two and $ρ\colon π_1(Σ) \to G$ a Hitchin representation into $G=\text{PSL}(n,\mathbb{R})$, $\text{PSp}(2n,\mathbb{R})$, $\text{PSO}(n,n+1)$ or $\text{G}_2$. We consider the energy functional $E$ on the Teichmüller space of $Σ$ which assigns to each point in $\mathcal{T}(Σ)$ the energy of the associated $ρ$-equivariant harmonic map. The main result of this paper is that $E$ is strictly plurisubharmonic. As a corollary we obtain an upper bound of $3 \cdot \text{genus}(Σ) -3$ on the index of any critical point of the energy functional.
