On a conjecture of Nitsche
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- by Gregory D. Crow PDF
- Proc. Amer. Math. Soc. 114 (1992), 1063-1068 Request permission
Abstract:
We show that under the hypothesis of bounded Gaussian curvature, certain minimal surfaces are in fact of finite total curvature. We can then answer the following version of a conjecture of Nitsche (J. Math. Mech. 11 (1962), 295) under the hypothesis of bounded Gaussian curvature: Conjecture. Let ${M^2} \subset {{\mathbf {R}}^3}$ be a complete minimal surface such that for some height function $H$, the level sets are (compact) Jordan curves. Then $M$ is a catenoid.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 114 (1992), 1063-1068
- MSC: Primary 53A10
- DOI: https://doi.org/10.1090/S0002-9939-1992-1105038-2
- MathSciNet review: 1105038