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Rigidity of Asymptotically Hyperbolic Manifolds

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Abstract

In this paper, we prove a rigidity theorem of asymptotically hyperbolic manifolds only under the assumptions on curvature. Its proof is based on analyzing asymptotic structures of such manifolds at infinity and a volume comparison theorem.

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Authors and Affiliations

  1. Key Laboratory of Pure and Applied Mathematics, School of Mathematics Science, Peking University, Beijing, 100871, P.R. China

    Yuguang Shi & Gang Tian

  2. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Gang Tian

  3. Department of Mathematics, Princeton University, Princeton, NJ, 08544, USA

    Gang Tian

Authors
  1. Yuguang Shi
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  2. Gang Tian
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Corresponding author

Correspondence to Gang Tian.

Additional information

Communicated by P. Sarnak

The first author’s research is partially supported by NSF grant of China.

The second author’s research is partially supported by an NSF grant and a Simon fund.

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Shi, Y., Tian, G. Rigidity of Asymptotically Hyperbolic Manifolds. Commun. Math. Phys. 259, 545–559 (2005). https://doi.org/10.1007/s00220-005-1370-1

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  • DOI: https://doi.org/10.1007/s00220-005-1370-1

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