First eigenvalue of symmetric minimal surfaces in $\mathbb{S}^3$ Jaigyoung ChoeMarc Soret 49Q0535J0553A10Laplacianeigenvalueminimal surface Let $\lambda_1$ be the first nontrivial eigenvalue of the Laplacian on a compact surface without boundary. We show that $\lambda_1=2$ on compact embedded minimal surfaces in $\mathbb{S}^3$ which are invariant under a finite group of reflections and whose fundamental piece is simply connected and has less than six edges. In particular $\lambda_1=2 $ on compact embedded minimal surfaces in $\mathbb{S}^3$ that are constructed by Lawson and by Karcher-Pinkall-Sterling. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3192 10.1512/iumj.2009.58.3192 en Indiana Univ. Math. J. 58 (2009) 269 - 282 state-of-the-art mathematics http://iumj.org/access/