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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The nonexistence of some noncompact constant mean curvature surfaces


Author: Leung-Fu Cheung
Journal: Proc. Amer. Math. Soc. 121 (1994), 1207-1209
MSC: Primary 53A10; Secondary 53C42
DOI: https://doi.org/10.1090/S0002-9939-1994-1186985-4
MathSciNet review: 1186985
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Abstract: Using isoperimetric inequality, we prove that there are no complete noncompact surfaces in $ {\mathbb{R}^3}$ with finite total curvature, odd Euler characteristic, and mean curvature bounded away from zero.


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DOI: https://doi.org/10.1090/S0002-9939-1994-1186985-4
Article copyright: © Copyright 1994 American Mathematical Society