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 $\Omega$ in Euclidean space in terms of the isoperimetric ratio ${\rm Vol}(\bd\Omega)/{\rm Vol}(\Omega)$. 
Simon Raulot (LMRS), Alessandro Savo (MeMoMat)
math.DG