Transition operators on co-compact \(G\)-spaces
The authors prove the following result: Let \(M\) be a complete, co-compact Riemannian manifold. Then \(0\) is in the \(L^2\)-spectrum of the Laplacian of \(M\) if and only if some (equivalently, every) closed quasi-transitive group of isometries of \(M\) is both amenable and unimodular. The same result holds also for Euclidean simplicial complexes.
scientific article; zbMATH DE number 5149118
scientific article