A symmetry condition for genus zero free boundary minimal surfaces attaining the first eigenvalue of one
Abstract
An embedded free boundary minimal surface in the 3-ball has a Steklov eigenvalue of one due to its coordinate functions. Fraser and Li conjectured that whether one is the first nonzero Steklov eigenvalue. In this paper, we show that if an embedded free boundary minimal surface of genus zero, with n boundary components, in the 3-ball has n distinct reflection planes, then one is the first eigenvalue of the surface.
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