论文标题
Hessian of Hausdorff dimension纯粹是虚构的方向
Hessian of Hausdorff dimension on purely imaginary directions
论文作者
论文摘要
我们将Bridgeman-Taylor和McMullen的经典结果扩展到了准河口空间上的Hausdorff Dimensian的Hessian上，以（1,1,1,2）-HyperConvex表示，Arxiv中介绍的课程：1902.01303介绍的课程，其中包括Hitchin表示的小型复杂形式的小型复杂形式和$ ch $θ$ -cosise $ -possive。我们还证明，当包含$γ\ po（n，1）\ to pu（n，1）$的Hausdorff尺寸的Hessian设置的限制限制的限制限制是积极的，当$γ$在$ po（n，1）$中共同处理时（除非$ n = 2 $，否则将变形与$ \ nath $ \ nath Formormation comprantiand po（n = 2 $）。
We extend classical results of Bridgeman-Taylor and McMullen on the Hessian of the Hausdorff dimension on quasi-Fuchsian space to the class of (1,1,2)-hyperconvex representations, a class introduced in arXiv:1902.01303 which includes small complex deformations of Hitchin representations and of $Θ$-positive representations. We also prove that the Hessian of the Hausdorff dimension of the limit set at the inclusion $Γ\to PO(n,1) \to PU(n,1)$ is positive definite when $Γ$ is co-compact in $PO(n,1)$ (unless $n=2$ and the deformation is tangent to $\mathfrak{X}(Γ,PO(2,1))).$
