Vol. 312, No. 1, 2021

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A nonexistence result for CMC surfaces in hyperbolic 3-manifolds

William H. Meeks III and Álvaro K. Ramos

Vol. 312 (2021), No. 1, 171–175
Abstract

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.

Keywords
constant mean curvature, hyperbolic 3-manifolds, Calabi-Yau problem
Mathematical Subject Classification
Primary: 53A10
Secondary: 49Q05, 53C42
Milestones
Received: 9 July 2020
Revised: 3 April 2021
Accepted: 5 April 2021
Published: 4 August 2021
Authors
William H. Meeks III
University of Massachusetts
Amherst, MA
United States
Álvaro K. Ramos
Universidade Federal do Rio Grande do Sul
Porto Alegre
Brazil