论文标题
立方差异和建筑物的限制
Limits of Cubic Differentials and Buildings
论文作者
论文摘要
在表面组表示的Hitchin成分中的Labourie-Loftin参数化中，我们证明了沿射线的全能渐近公式，该公式是跨射线的局部不变性的，可以定义该射线。在全球范围内，我们表明，对称的对称空间的相应的谐波映射家族将谐波图收敛于该空间的渐近锥。图像的几何形状也可以通过这种差异来描述：它是弱凸和（三分之一）的翻译表面。我们针对尊重Hitchin差异参数化的三角形组在此设置中定义了Hitchin组件的压缩。
In the Labourie-Loftin parametrization of the Hitchin component of surface group representations into SL(3,R), we prove an asymptotic formula for holonomy along rays in terms of local invariants of the holomorphic differential defining that ray. Globally, we show that the corresponding family of equivariant harmonic maps to a symmetric space converge to a harmonic map into the asymptotic cone of that space. The geometry of the image may also be described by that differential: it is weakly convex and a (one-third) translation surface. We define a compactification of the Hitchin component in this setting for triangle groups that respects the parametrization by Hitchin differentials.
