论文标题
爱因斯坦指标的稳定性和在较大的hempel距离内有效倍增
Stability of Einstein metrics and effective hyperbolization in large Hempel distance
论文作者
论文摘要
扩展了田的早期工作，我们表明，如果一个流形在适当意义上几乎是双曲线的度量，那么就存在一个爱因斯坦度量标准，即在$ c^{2，α} $拓扑中接近给定指标。在尺寸$ 3 $中，原始歧管只需要具有有限的体积，并且该卷可以任意大。应用程序包括新的证明$ 3 $ - 大hempel距离的叠加倍数，从而在双曲线度量标准上获得了一些新的几何控制，以及dehn填充和钻孔的分析证明，可以填充和钻孔许多尖端和管子。
Extending earlier work of Tian, we show that if a manifold admits a metric that is almost hyperbolic in a suitable sense, then there exists an Einstein metric that is close to the given metric in the $C^{2,α}$-topology. In dimension $3$ the original manifold only needs to have finite volume, and the volume can be arbitrarily large. Applications include a new proof of the hyperbolization of $3$-manifolds of large Hempel distance yielding some new geometric control on the hyperbolic metric, and an analytic proof of Dehn filling and drilling that allows the filling and drilling of arbitrary many cusps and tubes.
