Ein Hodge‐Satz für Mannigfaltigkeiten mit nicht‐glattem Rand

摘要

AbstractIn this paper the question of determining the dimension of the space of harmonic Dirichlet and Neumann differential forms on a Riemannian manifold with non‐smooth boundary is answered for a wide class of boundaries. The admissible boundaries can be characterized using a generalized “global segment property”. The well‐known relation between the Betti numbers and the dimension of these spaces is established in this more general case, too. Bounded and non‐bounded manifolds are treated (“exterior and interio