Rigidity and positivity of mass for asymptotically hyperbolic manifolds
Rigidity and positivity of mass for asymptotically hyperbolic manifolds
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DOI：
10.1007/s00023-007-0348-2
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发表时间：
2008-01-01
影响因子：
1.5
通讯作者：
Calloway, Gregory J.
中科院分区：
文献类型：
--
作者：
Andersson, Lars;Cai, Mingliang;Calloway, Gregory J.
多年来，维滕旋量的论点已被改编成几部作品，以证明积极的质量在渐近AdS和渐近双曲设置在任意尺寸。在本文中，我们证明了一个标量曲率刚性结果和一个正质量定理的渐近双曲流形，不需要自旋假设。正质量定理通过在共形边界附近的变形构造而化为刚性情形。刚性结果的证明是基于对BPS膜作用极小元的研究。
The Witten spinorial argument has been adapted in several works over the years to prove positivity of mass in the asymptotically AdS and asymptotically hyperbolic settings in arbitrary dimensions. In this paper we prove a scalar curvature rigidity result and a positive mass theorem for asymptotically hyperbolic manifolds that do not require a spin assumption. The positive mass theorem is reduced to the rigidity case by a deformation construction near the conformal boundary. The proof of the rigidity result is based on a study of minimizers of the BPS brane action.