论文标题
循环希格斯束和最小的表面
Cyclic Higgs bundles and minimal surfaces in pseudo-hyperbolic spaces
论文作者
论文摘要
我们在伪杂化的空间中介绍了一种最小表面$ \ MATHBB {h}^{n，n} $（带有$ n $偶数）或$ \ mathbb {h}^{n+1，n+1，n-1，n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $）nig nig nig nig nig nig n n+n+n;通过建立这些表面的无限刚性，我们获得了$ \ mathrm {so} _0（n，n+1）$的新证明，该理论的理论是，整体映射限制了对Hitchin基地的环境中的沉浸式限制的，并将其扩展到Collier的组成部分。这意味着劳里（Labourie）在杰出的$ g_2'$的情况下，劳里（Labourie）的前猜想是，我们还表明，这些最小表面是$ \ boldsymbol {j} $ - 几乎复杂的$ \ mathbb {h}^h}^{4,2} $的特定类型的全态曲线。
We introduce a type of minimal surface in the pseudo-hyperbolic space $\mathbb{H}^{n,n}$ (with $n$ even) or $\mathbb{H}^{n+1,n-1}$ (with $n$ odd) associated to cyclic $\mathrm{SO}_0(n,n+1)$-Higg bundles. By establishing the infinitesimal rigidity of these surfaces, we get a new proof, for $\mathrm{SO}_0(n,n+1)$, of Labourie's theorem that the holonomy map restricts to an immersion on the cyclic locus of Hitchin base, and extend it to Collier's components. This implies Labourie's former conjecture in the case of the exceptional group $G_2'$, for which we also show that these minimal surfaces are $\boldsymbol{J}$-holomorphic curves of a particular type in the almost complex $\mathbb{H}^{4,2}$.
