Asymptotically Hyperbolic Manifolds with Small Mass

作者：Dahl Mattias^*; Gicquaud Romain; Sakovich Anna

来源：Communications in Mathematical Physics, 2014, 325(2): 757-801.

DOI：10.1007/s00220-013-1827-6

For asymptotically hyperbolic manifolds of dimension n with scalar curvature at least equal to -n(n - 1) the conjectured positive mass theorem states that the mass is non-negative, and vanishes only if the manifold is isometric to hyperbolic space. In this paper we study asymptotically hyperbolic manifolds which are also conformally hyperbolic outside a ball of fixed radius, and for which the positive mass theorem holds. For such manifolds we show that the conformal factor tends to one as the mass tends to zero.

• 出版日期2014-1