599 research outputs found
Computing asymptotic invariants with the Ricci tensor on asymptotically flat and hyperbolic manifolds
We prove in a simple and coordinate-free way the equivalence bteween the
classical definitions of the mass or the center of mass of an asymptotically
flat manifold and their alternative definitions depending on the Ricci tensor
and conformal Killing fields. This enables us to prove an analogous statement
in the asymptotically hyperbolic case.Comment: Accepted for publication in Annales Henri Poincar{\'e
Universal positive mass theorems
In this paper, we develop a general study of contributions at infinity of
Bochner-Weitzenb\"ock-type formulas on asymptotically flat manifolds, inspired
by Witten's proof of the positive mass theorem. As an application, we show that
similar proofs can be obtained in a much more general setting as any choice of
an irreducible natural bundle and a very large choice of first-order operators
may lead to a positive mass theorem along the same lines if the necessary
curvature conditions are satisfied.Comment: Communications in Mathematical Physics, Springer Verlag, 2016, to
appea
Rigidity at infinity for even-dimensional asymptotically complex hyperbolic spaces
Any Kaehler metric on the ball which is strongly asymptotic to complex
hyperbolic space and whose scalar curvature is no less than the one of the
complex hyperbolic space must be isometrically biholomorphic to it. This result
has been known for some time in odd complex dimension and we provide here a
proof in even dimension.Comment: 10 page
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