IUMJ

Title: First eigenvalue of symmetric minimal surfaces in $\mathbb{S}^3$

Authors: Jaigyoung Choe and Marc Soret

Issue: Volume 58 (2009), Issue 1, 269-282

Abstract:

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.