A Characterization of the Critical Catenoid
نویسندگان
چکیده
We show that an embedded minimal annulus Σ ⊂ B which intersects ∂B orthogonally and is invariant under reflection through the coordinate planes is the critical catenoid. The proof uses nodal domain arguments and a characterization, due to Fraser and Schoen, of the critical catenoid as the unique free boundary minimal annulus in Bn with lowest Steklov eigenvalue equal to 1. We also give more general criteria which imply that a free boundary minimal surface in B invariant under a group of reflections has lowest Steklov eigenvalue 1.
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