A compact imbedding result on Lipschitz manifolds (Q752408)

The paper gives a new proof of the compact imbedding of the \(L_ p(M)\)- domain of the de Rham operator \((d+\delta)\) into \(L_ 2(M)\), the space of square-integrable differential forms on a closed Lipschitz manifold M. Hodge theory and properties of signature operators are derived as elementary consequences of the imbedding result. The approach is based on the observation of invariance properties of this compactness result, which eventually allows for reduction to the case of smooth M. Only basic concepts from functional analysis of Hilbert spaces are employed.