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Asymptotically hyperbolic metrics on the unit ball with horizons

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Abstract

In this paper, we construct a family of three-dimensional asymptotically hyperbolic manifolds with horizons and with scalar curvature equal to −6. The manifolds we construct can be arbitrarily close to anti-de Sitter-Schwarzschild manifolds at infinity. Hence, the mass of our manifolds can be very large or very small. The main arguments we use in this paper are gluing methods which are used by Miao in (Proc Am Math Soc 132(1):217–222, 2004).

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Authors and Affiliations

  1. Key Laboratory of Pure and Applied Mathematics, School of Mathematics Science, Peking University, Beijing, 100871, People’s Republic of China

    Yuguang Shi

  2. Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, China

    Luen-Fai Tam

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  1. Yuguang Shi
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  2. Luen-Fai Tam
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Correspondence to Yuguang Shi.

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Shi, Y., Tam, LF. Asymptotically hyperbolic metrics on the unit ball with horizons. manuscripta math. 122, 97–117 (2007). https://doi.org/10.1007/s00229-006-0057-z

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  • DOI: https://doi.org/10.1007/s00229-006-0057-z

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