The mass of asymptotically hyperbolic Riemannian manifolds

Piotr T. Chruściel, Marc Herzlich
2003 Pacific Journal of Mathematics  
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
more » ... mal completions of conformally compactifiable manifolds are unique.
doi:10.2140/pjm.2003.212.231 fatcat:bnw46ps44bg2hmel5s4esfruoe