Abstract
In this paper we prove a conjecture of Alexander and Currier that states, except for covering maps of equidistant surfaces in hyperbolic 3-space, a complete, nonnegatively curved immersed hypersurface in hyperbolic space is necessarily properly embedded.
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Acknowledgements
The authors would like to express their gratitude to Professor Jose Espinar at IMPA for his interest in this work. We are very appreciative of his careful reading that led to the current version.
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Communicated by F. C. Marques.
Shiguang Ma is support by NSFC Grant no.11301284 and NSFC Grant no.11571185. Jie Qing is partially supported by NSF DMS-1303543.
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Bonini, V., Ma, S. & Qing, J. On nonnegatively curved hypersurfaces in \(\mathbb {H}^{n+1}\). Math. Ann. 372, 1103–1120 (2018). https://doi.org/10.1007/s00208-018-1694-8
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DOI: https://doi.org/10.1007/s00208-018-1694-8