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.
Citation
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
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