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Harmonic maps and the topology of conformally compact Einstein manifolds

Conan Leung Chinese Univ of HK Tom Wan Chinese Univ of HK

Differential Geometry mathscidoc:1608.10096

MRL, 8, 801-812, 2001
We study the topology of a complete asymptotically hyperbolic Einstein manifold of which its conformal boundary has positive Yamabe invariant. We prove that all maps from such manifold into any nonpositively curved manifold are homotopically trivial. Our proof is based on a Bochner type argument on harmonic maps.
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@inproceedings{conan2001harmonic,
  title={Harmonic maps and the topology of conformally compact Einstein manifolds},
  author={Conan Leung, and Tom Wan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160831143539624221578},
  booktitle={MRL},
  volume={8},
  pages={801-812},
  year={2001},
}
Conan Leung, and Tom Wan. Harmonic maps and the topology of conformally compact Einstein manifolds. 2001. Vol. 8. In MRL. pp.801-812. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160831143539624221578.
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