Asymptotically hyperbolic metrics on the unit ball with horizons |
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| Authors: | Yuguang Shi Luen-Fai Tam |
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| Institution: | (1) Key Laboratory of Pure and Applied Mathematics, School of Mathematics Science, Peking University, Beijing, 100871, People’s Republic of China;(2) Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, China |
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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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| Keywords: | Primary 83C57 Secondary 53C44 |
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