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The mass of asymptotically hyperbolic Riemannian manifolds

Piotr T. Chrusciel·Marc Herzlich
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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.

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Piotr T. Chrusciel, Marc Herzlich. 2003-10-13. The mass of asymptotically hyperbolic Riemannian manifolds. https://arxiv.org/abs/math/0110035

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