Steklov Eigenvalues of Nearly Spherical Domains

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