A variational characterization of the catenoid
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526_2012_Article_579.pdf
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Author(s)
Bernstein, Jacob
Breiner, Christine Elaine
Date Issued
December 2012
Journal
Calculus of Variations and Partial Differential Equations
Publisher
Springer-Verlag
Citation
Bernstein, Jacob, and Christine Breiner. “A Variational Characterization of the Catenoid.” Calculus of Variations and Partial Differential Equations, vol. 49, no. 1–2, December 2012, pp. 215–232.
Version
Author's final manuscript
Abstract
In this note, we use a result of Osserman and Schiffer (Arch. Rational Mech. Anal. 58:285–307, 1975) to give a variational characterization of the catenoid. Namely, we show that subsets of the catenoid minimize area within a geometrically natural class of minimal annuli. To the best of our knowledge, this fact has gone unremarked upon in the literature. As an application of the techniques, we give a sharp condition on the lengths of a pair of connected, simple closed curves σ1 and σ2 lying in parallel planes that precludes the existence of a connected minimal surface Σ with ∂Σ=σ1∪σ2.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00526-012-0579-z
