Abstract
We show that the two closed boundary curves of a minimal annulus in a slab are both convex if one of them is convex and along the other curve the surface meets the plane at a constant angle. And therefore, under the same condition, the minimal annulus is foliated by convex planar curves all of which are parallel to the boundary. In particular, if the convex curve is a circle, then the annulus is part of a catenoid.
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This work was supported by a 2-Year Research Grant of Pusan National University.
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Pyo, J. Remarks on minimal annuli in a slab. Arch. Math. 98, 193–198 (2012). https://doi.org/10.1007/s00013-011-0349-8
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DOI: https://doi.org/10.1007/s00013-011-0349-8