Geometric Criteria for Essential Self-Adjointness of Discrete Hodge Laplacians on Weighted Simplicial Complexes

In this paper, we define the structure of $n$-simplicial complex, we consider generalizations of the Laplacians to simplicial complexes of higher dimension and we develop the notion of $\chi$-completeness for simplicial complexes. Otherwise, we study essential self-adjointness from the $\chi$-completeness geometric hypothesis.