On the rigidity for conformally compact Einstein manifolds

Details On the rigidity for conformally compact Einstein manifolds On the rigidity for conformally compact Einstein manifolds

2003-05-06

arxiv.org/abs/math/0305084v1

IMRN 2003, no. 21, 1141-1153

Mathematics

Differential Geometry

13 pages

Scientific paper

In this paper we prove that a conformally compact Einstein manifold with the round sphere as its conformal infinity has to be the hyperbolic space. We do not assume the manifolds to be spin, but our approach relies on the positive mass theorem for asymptotic flat manifolds. The proof is based on understanding of positive eigenfunctions and compactifications obtained by positive eigenfunctions.

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