论文标题
双曲线空间中抛物线多面体的二面刚度
Dihedral rigidity of parabolic polyhedrons in hyperbolic spaces
论文作者
论文摘要
在本说明中，我们建立了二面性刚度现象，用于双曲线歧管中的holosphers包围的抛物线多面体的集合，从而将Gromov的比较理论扩展到具有负标态曲率下限的指标。我们的结果是渐近双曲线歧管的阳性质量定理的定位。 我们还激励和提出了一些有关相关刚性现象和具有标态曲率下限的指标的收敛性的开放问题。
In this note, we establish the dihedral rigidity phenomenon for a collection of parabolic polyhedrons enclosed by horospheres in hyperbolic manifolds, extending Gromov's comparison theory to metrics with negative scalar curvature lower bounds. Our result is a localization of the positive mass theorem for asymptotically hyperbolic manifolds. We also motivate and formulate some open questions concerning related rigidity phenomenon and convergence of metrics with scalar curvature lower bounds.
