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Isometric immersions from the hyperbolic space |
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| Authors: | Hu Ze-Jun Zhao Guo-Song |
| Affiliation: | Department of Mathematics, Zhengzhou University, Zhengzhou, 450052, Henan, People's Republic of China ; Department of Mathematics, Sichuan University, Chengdu, 610064, Sichuan, People's Republic of China |
| Abstract: | In this paper, we transform the problem of determining isometric immersions from  into  into that of solving a degenerate Monge-Ampère equation on the unit disc. By presenting one family of special solutions to the equation, we obtain a great many noncongruent examples of such isometric immersions with or without umbilic set. |
| Keywords: | Isometric immersion hyperbolic space Monge-Amp`ere equation |
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