The renormalized volume and the volume of the convex core of quasifuchsian manifolds
The renormalized volume and the volume of the convex core of quasifuchsian manifolds
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拟福克流形的重正化体积和凸核体积
DOI：
10.4310/mrl.2013.v20.n4.a12
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Jean
中科院分区：
文献类型：
--
作者：
Jean
我们证明了一个拟fuchsian双曲3-流形的重整化体积等于它的凸核的体积，直到一个加法常数。我们还提供了一个精确的上限重整化体积的Weil-Petersson距离之间的共形结构在无穷远。由此证明了Teichm\“uller空间中的全纯圆盘只要足够大，就一定有“足够的”负曲率.
We show that the renormalized volume of a quasifuchsian hyperbolic 3-manifold is equal, up to an additive constant, to the volume of its convex core. We also provide a precise upper bound on the renormalized volume in terms of the Weil-Petersson distance between the conformal structures at infinity. As a consequence we show that holomorphic disks in Teichm\"uller space which are large enough must have "enough" negative curvature.