A Variational Characterization of the Catenoid
نویسندگان
چکیده
In this note, we use a result of Osserman and Schiffer [?] 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.
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