Determinant of the finite volume Laplacian (Q6142368)

This work provides one of the first tools for understanding definiteness of finite volume Laplacians in all dimensions and with a variety of duality structures. It is shown, in some cases, that the use of the determinant of the Laplacian restricted to each simplex to determine definiteness is possible. In a domain where the determinant is never zero, the Laplacian's definiteness will be the same throughout.