On the spectrum of the Dirichlet-to-Neumann operator acting on forms of a Euclidean domain

We compute the whole spectrum of the Dirichlet-to-Neumann operator acting on differential p-forms on the unit Euclidean ball. Then, we prove a new upper bound for its first eigenvalue on a domain Ω in Euclidean space in terms of the isoperimetric ratio V ol(∂Ω)/V ol(Ω).