  We consider the Dirichlet-to-Neumann operator (DNO) on nearly-circular and
nearly-spherical domains in two and three dimensions, respectively. Treating
such domains as perturbations of the ball, we prove the analyticity of the DNO
with respect to the domain perturbation parameter. Consequently, the Steklov
eigenvalues are also shown to be analytic in the domain perturbation parameter.
To obtain these results, we use the strategy of Nicholls and Nigam (2004); we
transform the equation on the perturbed domain to a ball and geometrically
bound the Neumann expansion of the transformed Dirichlet-to-Neumann operator.
