科研之友
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摘要
We show that an embedded minimal annulus Sigma(2) subset of B-3 which intersects partial derivative B-3 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 B-n with lowest Steklov eigenvalue equal to 1. We also give more general criteria which imply that a free boundary minimal surface in B-3 invariant under a group of reflections has lowest Steklov eigenvalue 1.
- 出版日期2018
