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A nonexistence result
for CMC surfaces in hyperbolic 3-manifolds
William H. Meeks III and Álvaro K. Ramos |
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Vol. 312 (2021), No. 1, 171–175
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Abstract |
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We prove that a complete hyperbolic 3-manifold of finite volume does not admit a properly embedded noncompact surface of finite topology with constant mean curvature greater than or equal to 1. |
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Keywords
constant mean curvature, hyperbolic 3-manifolds, Calabi-Yau
problem
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Mathematical Subject Classification
Primary: 53A10
Secondary: 49Q05, 53C42
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Milestones
Received: 9 July 2020
Revised: 3 April 2021
Accepted: 5 April 2021
Published: 4 August 2021
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Authors |
| William H. Meeks III | |
| University of Massachusetts Amherst, MA United States |
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| Álvaro K. Ramos | |
| Universidade Federal do Rio Grande
do Sul Porto Alegre Brazil |
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