论文标题
$ \ mathrm {sp}（4，\ mathbb {r}）$的平面最小表面具有多项式增长
Planar minimal surfaces with polynomial growth in the $\mathrm{Sp}(4, \mathbb{R})$-symmetric space
论文作者
论文摘要
我们研究了$ \ mathrm {sp}（4，\ mathbb {r}）$ - 对称空间中多项式生长的共形平面最小表面的渐近几何形状。我们描述了野生$ \ mathrm {sp}（4，\ mathbb {r}）$ - higgs捆绑$ \ mathbb {cp}^1 $与单个极点和轻度型电型多角色边界的最大值的组成部分之间的同构（4，\ mathbb {r}）$ - higgs捆绑在一起之间的同构同构（4，\ Mathbb {r}）$ - Higgs捆绑$ \ mathbb {h}^{2,2} $。此外，我们将这些表面识别为凸出的嵌入到$ \ Mathbb {r}^{4} $的Symplectic Planes的Grassmannian中。此外，我们还表明，我们的平面最大表面是与$ \ Mathrm {sp}（sp}（4，\ Mathbb {r}）相关的$ \ mathbb {h}^{2,2} $中最大表面的局部限制。
We study the asymptotic geometry of a family of conformally planar minimal surfaces with polynomial growth in the $\mathrm{Sp}(4,\mathbb{R})$-symmetric space. We describe a homeomomorphism between the "Hitchin component" of wild $\mathrm{Sp}(4,\mathbb{R})$-Higgs bundles over $\mathbb{CP}^1$ with a single pole at infinity and a component of maximal surfaces with light-like polygonal boundary in $\mathbb{H}^{2,2}$. Moreover, we identify those surfaces with convex embeddings into the Grassmannian of symplectic planes of $\mathbb{R}^{4}$. We show, in addition, that our planar maximal surfaces are the local limits of equivariant maximal surfaces in $\mathbb{H}^{2,2}$ associated to $\mathrm{Sp}(4,\mathbb{R})$-Hitchin representations along rays of holomorphic quartic differentials.
