论文标题
$ 2+1 $的大爆炸限制teichmüller空间的重力和瑟斯顿边界
Big-bang limit of $2+1$ gravity and Thurston boundary of Teichmüller space
论文作者
论文摘要
We study the asymptotic behavior of the solution curves of the dynamics of spacetimes of the topological type $Σ_{p}\times \mathbb{R}$, $p>1$, where $Σ_{p}$ is a closed Riemann surface of genus $p$, in the regime of $2+1$ dimensional classical general relativity.量规固定动力学的配置空间用teichmüller空间（$ \ Mathcal {t}σ_{p} \ of $σ_{p} $的$ \ MATHBB {p} \ oft \ Mathbb {r}^{6p-6} $）。利用某些谐波图的Dirichlet能量的属性，从相关的椭圆方程中得出的估计值以及紧凑型Riemann表面理论的一些标准结果，我们证明，每个非平凡的溶液曲线均脱离了TeichMülller的边缘。 （$ \ MATHCAL {PML} $ $ \ MATHCAL {PMF} $），Teichmüller空间的瑟斯顿边界。
We study the asymptotic behavior of the solution curves of the dynamics of spacetimes of the topological type $Σ_{p}\times \mathbb{R}$, $p>1$, where $Σ_{p}$ is a closed Riemann surface of genus $p$, in the regime of $2+1$ dimensional classical general relativity. The configuration space of the gauge fixed dynamics is identified with the Teichmüller space ($\mathcal{T}Σ_{p}\approx \mathbb{R}^{6p-6}$) of $Σ_{p}$. Utilizing the properties of the Dirichlet energy of certain harmonic maps, estimates derived from the associated elliptic equations in conjunction with a few standard results of the theory of the compact Riemann surfaces, we prove that every non-trivial solution curve runs off the edge of the Teichmüller space at the limit of the big bang singularity and approaches the space of projective measured laminations/foliations ($\mathcal{PML}$ $\mathcal{PMF}$), the Thurston boundary of the Teichmüller space.
