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Proceedings of the American Mathematical Society

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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.


References [Enhancements On Off] (What's this?)

  • [CD] M. Do Carmo and M. Dajzer, Helicoidal surfaces with constant mean curvature, Tôhoku Math. J. 34 (1982), 425-435. MR 676120 (84f:53003)
  • [LT] P. Li and L. F. Tam, Complete surfaces with fintie total curvature, J. Differential Geom. 33 (1991), 139-168. MR 1085138 (92e:53051)
  • [W] B. White, Complete surfaces of finite total curvature, J. Differential Geom. 26 (1987), 315-326. MR 906393 (88m:53020)

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Additional Information

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

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