Asymptotically Hyperbolic 3-Metric with Ricci flow foliation

Abstract

In general relativity, there have been a number of successful constructions for asymptotically flat metrics with a certain background foliation. In particular, C. -Y. Lin used a foliation by the Ricci flow on 2-spheres to establish an asymptotically flat extension and C. Sormani and Lin proved useful results with this extension. In this paper, we construct asymptotically hyperbolic 3-metrics with the Ricci flow foliation. We also study the rigid case when the Hawking mass of the inner surface of the manifold agrees with its total mass.

References in corpus (2)

• Almost Rigidity of the Positive Mass Theorem for Asymptotically Hyperbolic Manifolds with Spherical Symmetry
• Bartnik's mass and Hamilton's Modified Ricci Flow