Dirichlet-to-Neumann maps for differential forms on graphs and their eigenvalues

Abstract

In this paper, we first introduce Dirichlet-to-Neumann maps for differential forms on graphs which can be viewed as a discrete analogue of the corresponding Dirichlet-to-Neumann maps on compact Riemannian manifolds with boundary and a higher degree generalization of the Dirichlet-to-Neumann map on graphs introduced by Hua-Huang-Wang [14] and Hassannezhad-Miclo [11]. Then, some Raulot-Savo-type estimates on the eigenvalues of the DtN maps introduced are derived.