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1 April 2001 Complete properly embedded minimal surfaces in $\mathbf{R}^3$
Tobias H. Colding, William P. Minicozzi II
Duke Math. J. 107(2): 421-426 (1 April 2001). DOI: 10.1215/S0012-7094-01-10726-6

Abstract

In this short paper, we apply estimates and ideas from [CM4] to study the ends of a properly embedded complete minimal surface $Σ^{2} ⊂\mathbf{R}^{3}$ with finite topology. The main result is that any complete properly embedded minimal annulus that lies above a sufficiently narrow downward sloping cone must have finite total curvature.

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Tobias H. Colding. William P. Minicozzi II. "Complete properly embedded minimal surfaces in $\mathbf{R}^3$." Duke Math. J. 107 (2) 421 - 426, 1 April 2001. https://doi.org/10.1215/S0012-7094-01-10726-6

Information

Published: 1 April 2001
First available in Project Euclid: 5 August 2004

zbMATH: 1010.49025
MathSciNet: MR1823052
Digital Object Identifier: 10.1215/S0012-7094-01-10726-6

Subjects:
Primary: 53A10
Secondary: 53C21

Rights: Copyright © 2001 Duke University Press

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Vol.107 • No. 2 • 1 April 2001
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