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- W2952078045 abstract "In this note, we use a result of Osserman and Schiffer cite{OS} 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 $sigma_1$ and $sigma_2$ lying in parallel planes that precludes the existence of a connected minimal surface $Sigma$ with $partial Sigma=sigma_1cupsigma_2$." @default.
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- W2952078045 date "2010-12-17" @default.
- W2952078045 modified "2023-09-27" @default.
- W2952078045 title "A Variational Characterization of the Catenoid" @default.
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