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Proper harmonic maps between asymptotically hyperbolic manifolds

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Abstract

Generalizing the result of Li and Tam for the hyperbolic spaces, we prove an existence theorem on the Dirichlet problem for harmonic maps with \(C^1\) boundary conditions at infinity between asymptotically hyperbolic manifolds.

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Acknowledgments

The authors would like to thank Robin Graham and Man Chun Leung for their help during preparation of this article. They would also like to thank the anonymous referee for valuable comments. The second author would like to acknowledge the hospitality of the École normale supérieure, where he was visiting while the revision of the manuscript was carried out. The first author is supported in part by the Grant-in-Aid for Challenging Exploratory Research, Japan Society for the Promotion of Science, No. 24654009. The second author is supported in part by the Grant-in-Aid for JSPS Fellows, Japan Society for the Promotion of Science, No. 26-11754.

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Authors and Affiliations

  1. Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo, 152-8551, Japan

    Kazuo Akutagawa & Yoshihiko Matsumoto

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  1. Kazuo Akutagawa
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  2. Yoshihiko Matsumoto
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Correspondence to Yoshihiko Matsumoto.

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Akutagawa, K., Matsumoto, Y. Proper harmonic maps between asymptotically hyperbolic manifolds. Math. Ann. 364, 793–811 (2016). https://doi.org/10.1007/s00208-015-1229-5

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  • DOI: https://doi.org/10.1007/s00208-015-1229-5

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