The mass of asymptotically hyperbolic Riemannian manifolds

Piotr T. Chruściel and Marc Herzlich

Vol. 212 (2003), No. 2, 231–264

DOI: 10.2140/pjm.2003.212.231

Abstract

We present a set of global invariants, called “mass integrals", which can be defined for a large class of asymptotically hyperbolic Riemannian manifolds. When the “boundary at infinity" has spherical topology one single invariant is obtained, called the mass; we show positivity thereof. We apply the definition to conformally compactifiable manifolds, and show that the mass is completion-independent. We also prove the result, closely related to the problem at hand, that conformal completions of conformally compactifiable manifolds are unique.

Milestones

Received: 2 October 2001

Revised: 7 March 2003

Published: 1 December 2003