STEKLOV EIGENVALUES OF NEARLY SPHERICAL DOMAINS

We consider Steklov eigenvalues of three-dimensional, nearly spherical domains. In previous work, we have shown that the Steklov eigenvalues are analytic functions of the domain perturbation parameter. Here, we compute the first-order term of the asymptotic expansion, which can explicitly be written in terms of the Wigner 3-j symbols. We analyze the asymptotic expansion and prove the isoperimetric result that, if \ell is a square integer, the volume-normalized \ell th Steklov eigenvalue is stationary for a ball.

Automated summary

We investigate the Steklov eigenvalues of three-dimensional nearly spherical domains. Previous research has shown that these eigenvalues depend analytically on the domain perturbation parameter. In this study, we compute the first-order term of the asymptotic expansion using the Wigner 3-j symbols. We analyze the expansion and demonstrate the isoperimetric result that the volume-normalized \ell th Steklov eigenvalue is stationary for a ball when \ell is a perfect square.