On Fraser-Li conjecture with anti-prismatic symmetry and one boundary component

Let $\sigma _1$ be the first Steklov eigenvalue on an embedded free boundary minimal surface in $\b ^3$. We show that an embedded free boundary minimal surface $\Sigma_{\bf g}$ of genus $1 \leq {\bf g} \in \mathbb{N}$, one boundary component and anti-prismatic symmetry satisfy $\sigma_1 (\Sigma _{\bf g}) =1$. In particular, the family constructed by Kapouleas-Wiygul satisfies a such condition. This is a joint work with J.A. Gálvez and J. Pérez.